Completing Latin squares

Peter Horak, University of Washington at Tacoma

Some new and old problems concerned with completing Latin squares will be discussed. First we will focus on variations on P. Hall's theorem, e.g. completing Latin parallelepipeds, orthogonal Latin squares. Recent results on largest and smallest critical sets in Latin squares will be given. Finally we mention a problem on approximation of Latin squares by polynomials. Such Latin squares are used as a part of block cipher algorithms.

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