Random stuff

Unpublished fragments of work inspired by Ph.D. / M.Sc. theses of people nearby: Man, Erik, Tim, Ralf, Sander, Jochem ...


Man V. M. Nguyen wrote a thesis ("Computer-algebraic methods for the construction of designs of experiments") among other things about orthogonal arrays of strength 3. Part of that work was published:

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

Some data: Small orthogonal arrays of strength 3.


Erik Postma wrote a thesis ("Lie Algebras to Geometry and Back"). The note below proves a conjecture from Chapter 4 of that thesis.

Uniqueness of Lie orientation of Lie-orientable partial linear spaces.

(This note was incorporated in a 5-author draft

A.E. Brouwer, A.M. Cohen, H. Cuypers, J.I. Hall & E. Postma, Lie algebras, 2-groups and cotriangular spaces, Preprint July 2009. To appear in Advances in Geometry.)


Tim Mussche is working on a thesis, among other things about the chromatic number of the Kneser graph of a Grassmannian and that of the point-hyperplane flags. Results on the former have perhaps never been written down and will have to be reconstructed one day. The note below has some preliminary stuff on the latter.

Cocliques in the Kneser graph on point-hyperplane flags.


Ralf Gramlich wrote a thesis ("On Graphs, Geometries and Groups of Lie Type"). A preprint of that contained a characterization of graphs that are locally the point-hyperplane antiflag graph of a projective space in dimension at least 5. A prepreprint of a note that shows how to replace "at least 5" by "at least 3" in that proof:

Graphs that are locally the point-hyperplane antiflag graph of a projective space.

Ralf further simplified the proof, and the result can be seen in the final version of his thesis, and was also published in

A.M. Cohen, F.G.M.T. Cuypers, R. Gramlich, Local recognition of non-incident point-hyperplane graphs, Combinatorica 25 (2005) 271-296.


Sander van Rijnswou wrote a thesis ("Testing the equivalence of planar curves") that contained some discussion on the invariants of the planar quartic. As it turns out, one can give all invariants:

Invariants of the ternary quartic.

(In the same way one also gets invariants of binary forms.)


The M.Sc. thesis of Jochem Berndsen contains three parts. The third part computes gossip numbers. Here a slightly larger table.