AbstractsBiology & Animal Science

An Asymptotic Existence Theory on Incomplete Mutually Orthogonal Latin Squares

by Christopher Martin van Bommel

Institution: University of Victoria
Degree: MS
Year: 2015
Keywords: Latin square; Hole; Pairwise balanced design
Record ID: 2062130
Full text PDF: http://hdl.handle.net/1828/5930


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. Graduate