Algebraic Graph Theory Seminar - Christopher van Bommel

Tuesday, July 5, 2016 3:30 pm - 3:30 pm EDT (GMT -04:00)

Title: Mutually Orthogonal Latin Squares with Large Holes

Speaker: Christopher van Bommel
Affiliation: University of Waterloo
Room: MC 6486

Abstract:

An incomplete Latin square is a v x v array with an empty n x n subarray with every row and every column containing each symbol at most once and no row or column with an empty cell containing one of the last n symbols. A set of t incomplete mutually orthogonal Latin squares of order v and hole size n is a set of t incomplete Latin squares (containing the same empty subarray on the same set of symbols) with a natural extension to the condition of orthogonality. The existence of such sets have been previously explored only for small values of t. We determine an asymptotic result for the existence of t incomplete mutually orthogonal Latin squares for general t requiring large holes, which we develop from our results on incomplete pairwise balanced designs and incomplete group divisible designs.

No knowledge of design theory will be assumed. 

The talk is based on the author's master's thesis.