A. E. Brouwer - Available preprints


All papers here are copyrighted by their authors, and unmodified copies can be freely distributed by anyone. As far as I am aware, no commercial publisher holds any rights on any of these texts.


The links to the preprints below indicate the format. Links of type "Troff", "LaTeX", "PS" and perhaps "DVI" are moreover gzip-ped.

The "Troff" preprints will possibly enable you to guess at the text, but the infrastructure no longer exists to process them.

The preprints are sorted according to year of publication. Unpublished preprints according to the year they were written in.

This page is far from complete. Things not found here can sometimes be retrieved via Google scholar or found in the CWI repository. If you need something you cannot find, write to aeb@cwi.nl. There is also a list of publications.

Year: 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021


A. E. Brouwer & H. W. Lenstra, jr., Multiplicative division algorithms on the integers, Math. Centr. report ZN54, Amsterdam (Jun. 1973). PDF (scan)


A. E. Brouwer & A. Schrijver, On the period of an operator, defined on antichains, Math. Centr. report ZW24, Amsterdam (Jun. 1974). PDF (scan)

[A special case of the operation investigated here is that of Schutzenberger's promotion. The question posed is whether one has (the analog of) total promotion. In Problems, pp. 1190-1191 in: Combinatorics II, A. Hajnal & V. T. Sós (eds.), Proc. Keszthely 1976, Coll. Math. Soc. János Bolyai 18, North Holland, 1978, the authors ask whether the rectangle has total promotion. The affirmative answer is implicit in the work of Schutzenberger, and given very explicitly in M. Haiman, Dual equivalence with applications, including a conjecture of Proctor, Discr. Math. 99 (1992) 79-113, Theorem 4.4.]


A. E. Brouwer & A. Schrijver, Graphs with balanced star-hypergraph, Math. Centr. report ZW46, Amsterdam (Dec. 1975). PDF (scan)


A. E. Brouwer, A note on the covering of all triples on 7 points with Steiner triple systems, Math. Centr. report ZN63, Amsterdam (Feb. 1976). PDF (scan)

A. E. Brouwer, A connected metric space without nontrivial open connected subspaces, Math. Centr. report ZW83, Amsterdam (Aug. 1976). PDF (scan)

A. E. Brouwer, A generalization of Baranyai's theorem, Math. Centr. Report ZW81 (Aug. 1976). PDF (scan)


M. R. Best & A. E. Brouwer, The triply shortened binary Hamming code is optimal, Math. Centr. report ZW32, Amsterdam (Dec. 1975). (= Discrete Math. 17 (1977) 235-245.) PDF (scan)

Zs. Baranyai & A. E. Brouwer, Extensions of colourings of the edges of a complete (uniform hyper)graph, Math. Centr. report ZW91, Amsterdam (Feb. 1977). PDF (scan)

A. E. Brouwer, On the edge-colouring property for the hereditary closure of a complete uniform hypergraph, Math. Centr. report ZW95, Amsterdam (Apr. 1977). PDF (scan)

A. E. Brouwer, A new 5-design, Math. Centr. report ZW97, Amsterdam (May 1977). PDF (scan)

A. E. Brouwer, Some non-isomorphic BIBDs B(4,1;v), Math. Centr. report ZW102, Amsterdam (Oct 1977). PDF (scan)

A. E. Brouwer, Steiner triple systems without forbidden subconfigurations, Math. Centr. report ZW104, Amsterdam (Nov. 1977). Zbl 367.05011 PDF (scan)

[Lefmann et al., J. Combin. Des. 1 (1993) 379-394, point out that the lemma on p. 7 is false.]

A. E. Brouwer, The t-designs with v < 18, Math. Centr. report ZN76, Amsterdam (Aug. 1977). PDF (scan)

A. E. Brouwer, The uniqueness of the truncated affine plane of order five, Math. Centr. report ZN78, Amsterdam (Nov. 1977). PDF (scan)


A. E. Brouwer, On the packing of quadruples without common triples, Math. Centr. report ZW103, Amsterdam (Oct 1977). (= Ars Combinatoria 5 (1978) 3-6.) PDF (scan)


A. E. Brouwer, The number of mutually orthogonal Latin squares - a table up to order 10000, Math. Centr. report ZW123, Amsterdam (Jun. 1979). PDF (scan, 11MB)
[The "Added in proof" on p. 35 is not completely correct. For a modern version of these tables, see the Handbook of Combinatorics.]

A. E. Brouwer & A. M. Cohen, The Poincaré series of the polynomials invariant under SU2 in its irreducible representation of degree ≤17, Math. Centr. report ZW134, Amsterdam (Dec. 1979). Zbl 417.22008 PDF (scan)

A. E. Brouwer & M. Voorhoeve, Turán theory and the lotto problem, pp 99-105 in: Packing and Covering, A. Schrijver (ed.), Math. Centre Tracts 106, Amsterdam, 1979. Zbl 438.05025 PDF (scan)


A. E. Brouwer & A. W. J. Kolen, A super-balanced hypergraph has a nest point, Math. Centr. report ZW146/80, Amsterdam (Nov. 1980). PDF (scan)

A. E. Brouwer & P. J. Hoogendoorn, A note on ΓΔ-regular graphs, Math. Centr. report ZN98/80, Amsterdam (Nov. 1980). PDF (scan)


A. E. Brouwer, The linear spaces on 15 points, Math. Centr. report ZW 38/79, Sept. 1979. PDF (scan, 7MB) (= Ars Combinatoria 12 (1981) 3-35.)

A. E. Brouwer, On the size of a maximum transversal in a Steiner triple system, Math. Centr. report ZW 137/80, Amsterdam (Mar. 1980). (= Canad. J. Math. 33 (1981) 1202-1204.) PDF (scan)

A. E. Brouwer, An inequality in binary vector spaces, Math. Centr. report ZW150, Feb. 1981. MR 82c:05040; Zbl 448.51009 PDF (scan) (= Discrete Math. 59 (1986) 315-317. MR 87h:05051; Zbl 598.51010)

[Shows that if 2n has an irredundant cover by m affine subspaces with zero intersection, then m > n. Result rediscovered and generalized by Balázs Szegedy, Coverings of Abelian groups and vector spaces, JCT (A) 114 (2007) 20-34. For coverings of the real n-cube, see Noga Alon & Zoltán Füredi, Covering the Cube by Affine Hyperplanes, Eur. J. Comb. 14 (1993) 79-83.]

A. E. Brouwer, Some lotto numbers from an extension of Turán's theorem, Math. Centr. report ZW152, Amsterdam (Mar. 1981). PDF (scan)

A. E. Brouwer, The uniqueness of the near hexagon on 759 points, Math. Centr. report ZW154, Amsterdam (Mar. 1981). PDF (scan)

A. E. Brouwer, Some unitals on 28 points and their embeddings in projective planes of order 9, Math. Centr. report ZW155, Amsterdam (Mar. 1981). PDF (scan) (An updated version was published as pp 183-188 in: Geometries and groups (Proceedings Berlin 1981), M. Aigner & D. Jungnickel (eds.), Lecture Notes in Math. 893, Springer, Heidelberg 1981.)

A. E. Brouwer, The nonexistence of a regular near hexagon on 1408 points, Math. Centr. report ZW163, Amsterdam (Jul. 1981). PDF (scan)

[With appendix by AEB, H.A. Wilbrink & A.M. Cohen constructing a nonregular near hexagon on 1408 points.]

A. E. Brouwer & H. A. Wilbrink, Ovoids and fans in the generalized quadrangle GQ(4,2), Math. Centr. Report ZN102, Amsterdam (Oct. 1981) PDF (scan) (An updated version was published as Geom. Dedicata 36 (1990) 121-124.)


A. E. Brouwer, The Witt designs, Golay codes, and Mathieu groups, Troff preprint (1982) and a PDF version.

A. E. Brouwer, The uniqueness of the near hexagon on 729 points, Math. Centr. Report ZW162, Amsterdam (Jul. 1981) (= Combinatorica 2 (1982) 333-340.) PDF (scan)

A. E. Brouwer & J. H. van Lint, Strongly regular graphs and partial geometries, pp 85-122 in: Enumeration and Design - Proc. Silver Jubilee Conf. on Combinatorics, Waterloo, 1982, D. M. Jackson & S. A. Vanstone (eds.), Academic Press, Toronto, 1984. MR 87c:05033; Zbl 555.05016 PDF (scan)
Russian transl. in Kibern. Sb. Nov. Ser. 24 (1987) 186-229 Zbl 636.05013

[Correction: On p. 100, §7E, A construction by D. Taylor, it should say: ... the triples {x,y,z} for which H(x,y)H(y,z)H(z,x) is a square in GF(q^2) if q ≡ 3 mod 4, a nonsquare if q ≡ 1 mod 4.]


A. E. Brouwer & A. M. Cohen, Some remarks on Tits geometries, Indag. Math. 45 (1983) 393-402. (With an appendix by J. Tits.) PDF

A. E. Brouwer & A. M. Cohen, Computation of some parameters of Lie geometries, Math. Centr. report ZW198, Amsterdam (Sep. 1983). PDF (scan). PDF (modern version). Some form of this appeared in Algorithms in Combinatorial Design Theory, C. J. & M. J. Colbourn (eds.), North Holland, Amsterdam, 1985, pp. 1-48. See also HTML (June 2014).

A. E. Brouwer, A note on the uniqueness of the Johnson scheme, Math. Centr. report ZN 105/83, Amsterdam, 1983. PDF (scan)

A. E. Brouwer, The uniqueness of the strongly regular graph on 77 points, Math. Centr. report ZW147, Amsterdam (Nov 1980). (= J. Graph Th. 7 (1983) 455-461.) PDF (scan)

A. E. Brouwer & H. A. Wilbrink, Two infinite sequences of near polygons, Math. Centr. Report ZW194, Amsterdam (June 1983). PDF (scan)

A. E. Brouwer, On the uniqueness of a certain thin near octagon (or partial 2-geometry, or parallelism) derived from the binary Golay code, Math. Centr. report ZW196, Amsterdam (Jul. 1983). (= IEEE Trans. Inform. Th. IT-29 (1983) 370-371.) PDF (scan)

A. E. Brouwer, An infinite series of symmetric designs, Math. Centr. report ZW202, Amsterdam (Dec. 1983). PDF (scan)


A. Blokhuis & A. E. Brouwer, Uniqueness of a Zara graph on 126 points and non-existence of a completely regular two-graph on 288 points, pp. 6-19 in: Papers dedicated to J. J. Seidel, P. J. de Doelder, J. de Graaf & J. H. van Lint (eds.), Eindhoven Univ. Techn. report 84-WSK-03, Aug 1984. PDF


A. E. Brouwer, Recursive constructions of mutually orthogonal Latin squares, CWI Report PM-N8501, June 1985. PDF (scan). Some form of this appeared in Latin squares - new developments in the theory and applications, J. Dénes & A. D. Keedwell (eds.), North Holland, Amsterdam, 1991, pp. 149-168.

A. E. Brouwer, Chain calculus in the geometries of types An, Dn, E6, E7, E8, manuscript (1985). Troff. Converted from Troff to TeX and provided with a definition of Buekenhout-Tits diagram (2008). LaTeX and PDF.


A. E. Brouwer & A. M. Cohen, Local recognition of Tits geometries of classical type, Geom. Dedicata 20 (1986) 181-199. PDF

A. E. Brouwer, Uniqueness and nonexistence of some graphs related to M22, Graphs Combin. 2 (1986) 21-29. PDF (scan)


A. E. Brouwer & H. J. Veldman, Contractibility and NP-completeness, J. Graph Th. 11 (1987) 71-79. PDF (scan)

A. Blokhuis, A. E. Brouwer, A. Delandtsheer & J. Doyen, Orbits on Points and Lines in Finite Linear and Quasilinear Spaces, J. Combin. Th. (A) 44 (1987) 159-163. PDF


A. E. Brouwer & A. Neumaier, A remark on partial linear spaces of girth 5 with an application to strongly regular graphs, Combinatorica 8 (1988) 57-61. PDF (scan)


A. Blokhuis & A. E. Brouwer, Locally 4x4 grid graphs, J. Graph Th. 13 (1989) 229-244. PDF PDF (scan)

A. Blokhuis, A. E. Brouwer & H. A. Wilbrink, Heden's bound on maximal partial spreads, Discrete Math. 74 (1989) 335-339. PDF


A. Blokhuis, A. E. Brouwer & H. A. Wilbrink, Hermitian unitals are code words, Discrete Math. 97 (1991) 63-68. PDF


A. E. Brouwer & W. H. Haemers, Structure and uniqueness of the (81,20,1,6) strongly regular graph, Discrete Math. 106/107 (1992) 77-82. Troff.

A. E. Brouwer & C. A. van Eijl, On the p-rank of the adjacency matrices of strongly regular graphs, J. Alg. Comb. 1 (1992) 329-346. Troff.

[For some Smith Normal Forms, this note refers to the 2nd author's M.Sc. thesis.]

A. E. Brouwer, The uniqueness of the binary linear [27,7,12] code, 1 April 1992. Troff.

A. E. Brouwer, The composition factors of the Weyl modules with fundamental weights for the symplectic group. LaTeX.


A. E. Brouwer & L. M. G. M. Tolhuizen, A sharpening of the Johnson bound for binary linear codes and the nonexistence of linear codes with Preparata parameters, Designs, Codes & Cryptography 3 (1993) 95-98. Troff.


A. E. Brouwer, Finite graphs in which the point neighbourhoods are the maximal independent sets. LaTeX (with comment).


C. L. M. de Lange, Some new cyclotomic strongly regular graphs, J. Algebraic Combin. 4 (1995) 329-330. Troff.

A. E. Brouwer & W. H. Haemers, Association schemes, pp 747-771 in: Handbook of Combinatorics, R. Graham, M. Groetschel, L. Lov'asz, eds., Elsevier, 1995. Zbl 849.05072. Troff, PS.

A. E. Brouwer, Toughness and spectrum of a graph, Lin. Alg. Appl. 226-228 (1995) 267-271. LaTeX.

A. E. Brouwer, Variations on a theme by Weetman, Discrete Math. 138 (1995) 137-145. PDF.


A. E. Brouwer, Spectrum and connectivity of graphs, CWI Quarterly 9 (1996) 37-40. LaTeX.

A. Blokhuis, A. E. Brouwer & R. Riebeek, The spectrum of the van Leijenhorst matrix, 3 May 1996. LaTeX.


A. Blokhuis & A. E. Brouwer, Determination of the distance-regular graphs without 3-claws, Discrete Math. 163 (1997) 225-227. LaTeX.

A. E. Brouwer & H. M. Mulder, The vertex connectivity of a $\{0,2\}$-graph equals its degree, Discrete Math. 169 (1997) 153-155. LaTeX.

A. E. Brouwer, W. H. Haemers & V. D. Tonchev, Embedding Partial Geometries in Steiner Designs, pp. 33-41 in: Geometry, Combinatorial Designs and Related Structures, Proceedings of the First Pythagorean Conference, J. W. P. Hirschfeld, S. S. Magliveras, M. J. de Resmini (eds.), Cambridge University Press, 1997. LaTeX.


R. J. Blok & A. E. Brouwer, The geometry far from a residue, pp. 29-38 in: Groups and Geometries, L. di Martino, W. M. Kantor, G. Lunardon, A. Pasini, M. C. Tamburini (eds.), Birkhaüser Verlag, Basel, 1998. LaTeX.

[In fact F4(2) has 16, not 4, connected components far from a chamber. See R. J. Blok, On geometries related to buildings, thesis, 1999, Thm 3.33.]

A. E. Brouwer, H. O. Hämäläinen, P. R. J. Östergård & N. J. A. Sloane, Bounds on Mixed Binary/Ternary Codes, IEEE Trans. Inf. Th. 44 (1998) 140-161. LaTeX.

[Pedro Pablo Rivas Soriano points out that in Code C3 in Lemma 5.5 the last code word should be "01002" instead of "02010".]

A. E. Brouwer, J. H. Koolen & R. J. Riebeek, A new distance-regular graph associated to the Mathieu group M10, J. Alg. Comb. 8 (1998) 153-156. LaTeX.

A. E. Brouwer & R. J. Riebeek, The spectra of Coxeter graphs, J. Alg. Comb. 8 (1998) 15-28. LaTeX.

A. E. Brouwer & R. J. Riebeek, The spectrum of the second subconstituent of the bilinear forms graph $H_q(d,e)$, Europ. J. Combin. 19 (1998) 299-305. LaTeX. on-line.

A. E. Brouwer, Linear spaces of quadrics and new good codes, Bull. Belg. Math. Soc. 5 (1998) 177-180. LaTeX.

A. E. Brouwer, Partitioning into induced trees is NP-complete, 30 Oct 1998. LaTeX.


A. E. Brouwer & J. H. Koolen, The distance-regular graphs of valency four, J. Alg. Combin. 10 (1999) 5-24. LaTeX.

A. E. Brouwer, An associative block design $ABD(8,5)$, SIAM J. Comput. 28 (1999) 1970-1971 (electronic). LaTeX.

A. E. Brouwer, R. M. Wilson & Qing Xiang, Cyclotomy and Strongly Regular Graphs, J. Alg. Combin 10 (1999) 25-28. LaTeX.

A. Blokhuis & A. E. Brouwer, The universal embedding dimension of the near polygon on the 1-factors of a complete graph, Designs, Codes and Cryptography 17 (1999) 299-303. LaTeX.

A. E. Brouwer, R. Pellikaan & E. R. Verheul, Doing more with fewer bits, pp. 321-332 in Advances in Cryptology Asiacrypt '99, K. Y. Lam, E. Okamoto and C.-P. Xing, Eds., Lect. Notes Comp. Sci. 1716, Springer, Berlin 1999. PS, PDF.


A. E. Brouwer, Locally Paley graphs, Designs, Codes and Cryptography 21 (2000) 69-76. LaTeX.


G. T. Bogdanova, A. E. Brouwer, S. N. Kapralov & P. R. J. Östergård, Error-Correcting Codes over an Alphabet of Four Elements, Designs, Codes and Cryptography 23 (2001) 333-342. LaTeX.

J. H. Koolen, On a conjecture of Bannai and Ito. There are only finitely many distance-regular graphs of valency five, six or seven. LaTeX.


A. E. Brouwer, Zeilberger-Wilf theory (course notes). LaTeX, PostScript, PDF.
(See also A. E. Brouwer, Automatic summation using Zeilberger-Wilf theory, Nieuw Archief voor Wiskunde (Ser. 5) 3 (2002) 308-312.)

A. E. Brouwer, H. Cuypers & E. W. Lambeck, The hyperplanes of the $M_{24}$ near polygon, Graphs Combin. 18 (2002) 415-420. LaTeX.


A. Blokhuis & A. E. Brouwer, The universal embedding dimension of the binary symplectic dual polar space, Discrete Math. 264 (2003) 3-11. LaTeX.

A. Blokhuis, A. E. Brouwer & H. A. Wilbrink, Blocking sets in PG(2,p) for small p, and partial spreads in PG(3,7), Advances in Geometry, special issue (2003) S245-S253. LaTeX, PDF.

A. E. Brouwer, J. H. Koolen & M. H. Klin, A root graph that is locally the line graph of the Petersen graph, Discrete Math. 264 (2003) 13-24. DVI. on-line.

A. E. Brouwer, C. D. Godsil, J. H. Koolen & W. J. Martin, Width and dual width of subsets in polynomial association schemes, J. Combin. Theory (A) 102 (2003) 255-271. PDF.


A. Blokhuis & A. E. Brouwer, Small additive quaternary codes, Europ. J. Combin. 25 (2004) 161-167. LaTeX.


A. E. Brouwer & W. H. Haemers, Eigenvalues and perfect matchings, Lin. Alg. Appl. 395 (2005) 155-162. LaTeX.


A. E. Brouwer, P. J. Cameron, W. H. Haemers & D. A. Preece, Self-dual, not self-polar, Discr. Math. 306 (2006) 3051-3053. LaTeX, PDF.

A. E. Brouwer, A. M. Cohen, M. V. M. Nguyen, Fractional factorial designs of strength 3 and small run sizes (or Orthogonal arrays of strength 3 and small run sizes), J. Statist. Planning and Inference 136 (2006) 3268-3280. LaTeX, PDF.

A. E. Brouwer, Classification of small (0,2)-graphs, J. Combinatorial Th. (A) 113 (2006) 1636-1645. LaTeX, PDF.

A. E. Brouwer, Sudoku puzzles and how to solve them, html, PDF. (Versions have been published in Nieuw Archief Wisk. (Ser. 5) 7 (2006) 258-263 and in Newsletter of the European Math. Soc. 66 (Dec 2007) 13-17.)


Aart Blokhuis, Andries E. Brouwer & Willem H. Haemers, On 3-chromatic distance-regular graphs, Designs, Codes and Cryptography 44 (2007) 293-305. PDF. (DCC on-line.)

A. E. Brouwer, A(36,10,6) = 37, Nov. 2007, LaTeX, PDF.


A. E. Brouwer, A. Jurišić & J. H. Koolen, Characterization of the Patterson graph, J. Algebra 320 (2008) 1878-1886. DVI, PDF. (J. Algebra on-line.)

A. E. Brouwer & W. H. Haemers, The integral trees with spectral radius 3, Lin. Alg. Appl. 429 (2008) 2710-2718. LaTeX, PDF.

A. E. Brouwer, Small integral trees, Electr. J. Combin. 15 (2008) N1. LaTeX, PDF.

A. E. Brouwer, G. F. Post & G. J. Woeginger, Tight bounds for break minimization, J. Combin. Th. (A) 115 (2008) 1065-1068. Memorandum 1836 Univ. Twente, May 2007, PDF. (JCT (A) on-line.)

A. E. Brouwer & W. H. Haemers, Topics in algebraic graph theory (Lecture Notes for a course held in Tehran, Spring 2006), pp 1-66 in: Lectures on Combinatorics I, IPM Lecture Notes Series 8, Tehran, 2008. LaTeX.

A. E. Brouwer & W. H. Haemers, A lower bound for the Laplacian eigenvalues of a graph - proof of a conjecture by Guo, Lin. Alg. Appl. 429 (2008) 2131-2135. LaTeX, PDF. (LAA on-line.)

A. E. Brouwer & W. H. Haemers, Hamiltonian strongly regular graphs, Mar. 2008. Center for Economic Research Discussion paper 2008-28, Tilburg Univ. LaTeX, PDF
(This is weaker than the main result of Bigalke & Jung, Monatsh. Math. 88 (1979) 195-210.)

A. E. Brouwer, A construction of the Suzuki graph, LaTeX, PDF.
(This was a comment on a paper by Horiguchi, Kitazumi & Nakasora. A joint note was published in JCT (A), see below.)

A. E. Brouwer, The anticommutative Latin squares of order 8, Sept. 2008. PDF.
(Part of this work was done independently by Ian Wanless. A joint note "Universally noncommutative loops" appeared in Bull. Inst. Comb. Appl., see below. PDF.)


Andries E. Brouwer & Patric R. J. Östergård, Classification of the (0,2)-graphs of valency 8, Discr. Math. 309 (2009) 532-547. Preprint Jan 2007, LaTeX, DVI, PDF. (Discr. Math. on-line.)

A. E. Brouwer & J. H. Koolen, The vertex-connectivity of a distance-regular graph, Eur. J. Combin. 30 (2009) 668-673. Preprint July 2006. LaTeX. (Eur. J. Combin. on-line.)

Andries E. Brouwer, Naoyuki Horiguchi, Masaaki Kitazume & Hiroyuki Nakasora, A construction of the sporadic Suzuki graph from U3(4), J. Combin. Th. (A) 116 (2009) 1056-1062. (JCT (A) on-line.)
(See also the preprint mentioned above - PDF.)

A. E. Brouwer & E. Spence, Cospectral graphs on 12 vertices, Electr. J. Combin. 16(1) (2009) N20. (EJC PDF.) Preprint May 2009. PDF.

A. E. Brouwer, The number of dominating sets of a finite graph is odd, Preprint May 2009. LaTeX, PDF. Péter Csorba gave a topological proof, and Lex Schrijver gave a beautiful 1-line proof - see PDF with 3 proofs. Another version: PDF.

A. E. Brouwer, Integral trees homeomorphic to a double star, Preprint Sept 2009. PDF.
(This was a comment on a paper by Del-Vecchio, Jacobs, Trevisan and Vinagre. A joint note appeared as Bull. Inst. Comb. Appl. 61 (2011) 77-80.)


A. Blokhuis, A. E. Brouwer, A. Chowdhury, P. Frankl, T. Mussche, B. Patkós & T. Szőnyi, A Hilton-Milner theorem for vector spaces, Preprint July 2009. PDF. Preprint Oct 2009. PDF. Electr. J. Combin. 17 (2010) R71. (EJC PDF)

A. E. Brouwer & M. Popoviciu, The invariants of the binary nonic, J. Symbolic Computation 45 (2010) 709-720. (JSC on-line.) Preprint July 2009. PDF. arXiv.

A. E. Brouwer & M. Popoviciu, The invariants of the binary decimic, J. Symbolic Computation 45 (2010) 837-843. (JSC on-line.) Preprint Aug 2009. PDF. arXiv.

A. Blokhuis, A. E. Brouwer & T. Szőnyi, Covering all points except one, J. Algebr. Combin. 32 (2010) 59-66. Preprint Nov. 2008. LaTeX, PDF. Revised PDF. (JACO on-line, 15 Oct 2009.)

A. E. Brouwer, The eigenvalues of oppositeness graphs in buildings of spherical type, pp. 1-10 in: Combinatorics and Graphs, R. A. Brualdi, S. Hedayat, H. Kharaghani, G. B. Khosrovshahi, S. Shahriari (eds.), AMS Contemporary Mathematics Series 531, 2010. Preprint July 2009. PDF.


A. E. Brouwer & J. Draisma, Equivariant Gröbner bases and the Gaussian two-factor model, Mathematics of Computation 80 (2011) 1123-1133. Preprint Aug 2009. Preprint Jan 2010. arXiv.

A. E. Brouwer, R. R. Del-Vecchio, D. P. Jacobs, V. Trevisan & C. T. M. Vinagre, Integral trees homeomorphic to a double star, Bulletin of the ICA 61 (2011) 77-80.
(Cf. note Integral trees homeomorphic to a double star, 2009 above.)

A. E. Brouwer & I. M. Wanless, Universally noncommutative loops, Bulletin of the ICA 61 (2011) 113-115.
(Cf. note The anticommutative Latin squares of order 8, 2008 above.)

A. E. Brouwer & T. Etzion, Some new constant weight codes, Advances in Mathematics of Communications 5 (2011) 417-424. Preprint Dec 2009. There is also a machine-readable version of the data.

A. E. Brouwer & M. Popoviciu, SL2-modules of small homological dimension, Transformation Groups 16 (2011) 599-617. Preprint Oct. 2010. arXiv. on-line

A. Blokhuis, A. E. Brouwer, T. Szőnyi & Z. Weiner, On q-analogues and stability theorems, J. Geometry 101 (2011) 31-50. Preprint May 2011. on-line

A. E. Brouwer, Een paar gelijkmatig verdeelde codes, pp. 9-14 in: Klabotscript, Liber Amicorum voor Henk van Tilborg, 7 october 2011. PDF

[The 2F4(2) generalized octagon of order (4,2) does not have a perfect 1-error-correcting code.]


A. E. Brouwer & W. H. Haemers, Spectra of graphs, Springer, 2012. ISBN 978-1-4614-1938-9. Web page.

A. E. Brouwer, A. M. Cohen, H. Cuypers, J. I. Hall & E. Postma, Lie algebras, 2-groups and cotriangular spaces, Advances in Geometry 12 (2012) 1-17. PDF. on-line.

A. E. Brouwer, O. Olmez & S. Y. Song, Directed strongly regular graphs from 1½-designs, Europ. J. Comb. 33 (2012) 1174-1177. on-line. Preprint, old/Sep 2011.

A. E. Brouwer, J. E. Ducey & P. Sin, The elementary divisors of the incidence matrix of skew lines in PG(3,q), Proc. Amer. Math. Soc. 140 (2012) 2561-2573. Preprint 1 Mar 2011. arXiv. on-line

A. Blokhuis & A. E. Brouwer, Spectral characterization of a graph on the flags of the eleven point biplane. Designs, Codes & Cryptography 65 (2012) 65-69. on-line. Preprint (entitled Characterization of a graph by its spectrum), Apr 2011.

A. Blokhuis, A. E. Brouwer & W. H. Haemers, The graph with spectrum 141 240 (−4)10 (−6)9, Designs, Codes & Cryptography 65 (2012) 71-75. on-line. Preprint Mar 2011.

A. E. Brouwer & Ç. Güven, The generating rank of the space of short vectors in the Leech lattice mod 2, Designs, Codes & Cryptography 65 (2012) 107-113. on-line. Preprint, Aug 2008/Jul 2011.

A. Blokhuis, A. E. Brouwer & T. Szőnyi, On the chromatic number of q-Kneser graphs, Designs, Codes and Cryptography 65 (2012) 187-197. on-line. Preprint, Aug. 2010.

A. E. Brouwer & D. V. Pasechnik, Two distance-regular graphs, J. Algebr. Combin. 36 (2012) 403-407. (JACO on-line, 20 Dec 2011.) Preprint, Jun 2011. arXiv.

A. E. Brouwer & M. Popoviciu, Sylvester versus Gundelfinger, Sigma 8 (2012) 075, 7pp. on-line. Preprint, Apr 2011. arXiv.

A. E. Brouwer, The [32,10,12] TFCI code, manuscript, Jan 2012.


A. E. Brouwer & L. Chastkofsky, (0,2)-graphs and root systems, Preprint, Oct 2008/Aug 2012. Journal of Discrete Mathematics 2013, Article 140537, 4pp. on-line.

A. E. Brouwer (and C. F. Mills, W. H. Mills, A. Verbeek), Counting families of mutually intersecting sets, Electronic J. Combinatorics 20(2) (2013) #P8. Preprint, Aug/Dec 2012.

λ(9) = 423295099074735261880.
K(9,4) has 366996244568643864340 independent sets.
Λ(8) = 14704022144627161780744368338695925293142507520.
Λ(9) = 12553242487940503914363982718112298267975272720808010757809032705650591023015520462677475328.

A. E. Brouwer & J. Huizinga, A family of 2-arc transitive pentagraphs with unbounded valency, Innov. Incidence Geom. 13 (2013) 141-147. on-line. Preprint, April 1992, PDF.

A. E. Brouwer, Pessimal gossiping, Notes inspired by the Ph.D. defense of Bart Frenk, Mar 2013. (Improved version, Nov 2014.)

[See also the data for small n, an extension of the work of Jochem Berndsen.]

A. Blokhuis, A. E. Brouwer & T. Szőnyi, Proof of a conjecture by Đoković on the Poincaré series of the invariants of a binary form, Indagationes Math. 24 (2013) 766-773. Preprint Feb 2009/Nov 2012. (Indag. Math. on-line, Dec 2012.)

A. E. Brouwer, Counting zero-sum subsets of an abelian group, brief notes, Oct/Dec 2013.

A. E. Brouwer, Parameters of an association scheme, note, Dec 2013.

[F. Vanhove pointed out a mistake in BCN, Theorem 12.1.1. This note redoes his computation. Published in 2020.]


A. Blokhuis, A. E. Brouwer & Ç. Güven, Cocliques in the Kneser graph on the point-hyperplane flags of a projective space, Combinatorica 34 (2014) 1-10. Preprint Oct 2010. (Combinatorica on-line, Jan. 2014.)

A. Blokhuis, A. E. Brouwer & T. Szőnyi, Maximal cocliques in the Kneser graph on point-plane flags in PG(4,q), Europ. J. Comb. 35 (2014) 95-104. Preprint, Feb 2012. (EurJC on-line, July 2013.)

A. Blokhuis, A. E. Brouwer & A. Sali, Note on the size of binary Armstrong codes, Designs, Codes and Cryptography 71 (2014) 1-4. Preprint, Apr 2012. (DCC on-line, June 2012.)

A. E. Brouwer, R. Gow & J. Sheekey, Counting symmetric nilpotent matrices, Electr. J. Combin. 21 (2014) P2.4. Preprint, Mar 2012 / Mar 2013. (EJC on-line, Apr 2014.)

T. Jenrich & A. E. Brouwer, A 64-dimensional counterexample to Borsuk's conjecture, Electr. J. Combin. 21 (2014) P4.29. Preprint, Jan 2014. (EJC on-line, Nov 2014.)

L. Bedratyuk & A. E. Brouwer, Resolutions and Betti diagrams of algebras of SL2-invariants, C. R. Acad. Bulg. Sci. 67 (2014) 1477-1484. Preprint, Jul 2014.

aeb, Notes on Jenrich's srg(336,80,28,16), Sep 2014.


Andries E. Brouwer, Jan Draisma & Bart J. Frenk, Lossy gossip and composition of metrics, Discrete & Computational Geometry 53 (2015) 890-913. Preprint, Nov 2014. arXiv (v2). (DCG on-line, Feb 2015.)

A. Blokhuis, A. E. Brouwer, D. Jungnickel, V. Krčadinac, S. Rottey, L. Storme, T. Szőnyi & P. Vandendriessche, Blocking sets of the Hermitian unital, Preprint Oct 2013. Published as Blocking sets of the classical unital, Finite Fields Appl. 35 (2015) 1-15. (FFA, on-line, Mar 2015.)

A. Abiad, A. E. Brouwer, W. H. Haemers, Godsil-McKay switching and Isomorphism, Electronic Journal of Linear Algebra 28 (2015) 4-11. Preprint, May 2014. arXiv.

A. E. Brouwer & M. A. Fiol, Distance-regular graphs where the distance-d graph has fewer distinct eigenvalues, Lin. Alg. Appl. 480 (2015) 115-126. Preprint, Aug 2014. (LAA on-line, May 2015.)

aeb, Button Madness, May 2015. (A write-up with mathematics by Aart Blokhuis from 1994, and a recent table.)

A. E. Brouwer, J. Draisma & M. Popoviciu, The degrees of a system of parameters of the ring of invariants of a binary form, Transformation Groups 20 (2015) 953-967. preprint, Aug 2009/Apr 2014. arXiv. (TG on-line, Sep 2015.)


A. E. Brouwer, S. M. Cioabă, W. H. Haemers & J. R. Vermette, Notes on simplicial rook graphs, J. Algebraic Combin. 43 (2016) 783-799. preprint, Aug 2014. arXiv. (JAC on-line, Sep 2015.)

aeb, Strongly regular graphs from hyperovals, Feb 2016. (A description of a family of graphs due to Huang, Huang, and Lin.)

A. E. Brouwer, Nonexistence of a distance-regular graph, Preprint, 2016-06-22.

[This is half of the following note.]

A. E. Brouwer, Supalak Sumalroj & Chalermpong Worawannotai, The nonexistence of distance-regular graphs with intersection arrays {27,20,10;1,2,18} and {36,28,4;1,2,24}, Australasian J. Combin. 66 (2016) 330-332. (AJC on-line, Oct 2016.)

A. E. Brouwer, Regular symmetric Hadamard matrices with constant diagonal, Preprint, 2016-07-06.


A. Blokhuis & A. E. Brouwer, Cocliques in the Kneser graph on line-plane flags in PG(4,q), Combinatorica 37 (2017) 795-804. on-line, shared. Preprint Nov 2011/Jun 2013.

A. Blokhuis, A. E. Brouwer & B. M. M. de Weger, Binomial collisions and near collisions, Integers 17 (2017) #A64. (On-line PDF, Dec 2017.) Preprint, 2017-07-21. arXiv.

aeb, Szöllősi's equiangular system in R18, Apr 2017.


A. E. Brouwer & J. D. Christensen, Counterexamples to conjectures about Subset Takeaway and counting linear extensions of a Boolean lattice, Order 35 (2018) 275-281. arXiv. Preprint, 2017-05-03. (Order on-line, Jun 2017.)
The number of linear extensions of the partial order of the 7-cube equals

(This number factors as 217 * 32 * 5 * 7 * 11 * 137873 * 1237877 * 530282738441 * 19599757476499631400253492670595603436777 * 782594035644580169923794951943711324283631322562043550488764560987.)

Andries E. Brouwer, Sebastian M. Cioabă, Ferdinand Ihringer & Matt McGinnis, The smallest eigenvalues of Hamming graphs, Johnson graphs and other distance-regular graphs with classical parameters, J. Combin. Th. (B) 133 (2018) 88-121. Preprint 2017-09-26. arXiv. (JCT (B) on-line).


A. E. Brouwer & S. C. Polak, Uniqueness of codes using semidefinite programming, Designs, Codes and Cryptography 87 (2019) 1881-1895. arXiv. Preprint, 2017-09-07. (DCC on-line, Nov 2018.)


F. Vanhove, The association scheme on the points off a quadric, Bull. Belg. Math. Soc. Simon Stevin 27 (2020) 153-160. PDF.


A. E. Brouwer, Two-weight codes, Chapter 19, pp. 449-462, in Concise Encyclopedia of Coding Theory, W. C. Huffman, J.-L. Kim, P. Solé, eds., CRC Press, 2021. Preprint, Sept. 2018.

A. E. Brouwer & H. Van Maldeghem, fragments of a text on strongly regular graphs, srgw.pdf.

aeb, The 4-vertex condition - extended abstract, 2021-05-01.

Very brief version of the following note.

A. E. Brouwer, F. Ihringer & W. M. Kantor, Strongly regular graphs satisfying the 4-vertex condition, preprint, preliminary version, 2021-06-22.

A. E. Brouwer & W. J. Martin, Triple intersection numbers for the Paley graphs, preprint, 2021-09-05.

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