Presented by: 
Dr Sara Herke
Date: 
Tue 23 May, 2:00 pm - 3:00 pm
Venue: 
67-442

Abstract:
Finite projective planes are important structures in design theory and geometry. They are well-known to exist for prime power orders but the question of whether or not projective planes can exist for non-prime power orders remains one of the most important unsolved problems in combinatorics. There is an equivalence between finite projective planes and complete sets of mutually orthogonal Latin squares (MOLS). The useful notion of parity of permutations has been extended to Latin squares; in this talk, we consider a direct generalization of the parity of a Latin square to the parity of a set of MOLS. Our results give insight as to why it may be harder to build projective planes of order n >2 when n = 2 (mod 4). This is joint work with Nevena Francetic and Ian Wanless.