The Intersection Problem for Latin Squares with Holes of Size 2 and 3

Abstract

In this dissertation we give complete solutions for the intersection problem of latin squares with holes of size 2 and 3. For a pair of 2n x 2n latin squares with holes of size 2 to have k entries in common outside of the holes k E {0, 1, 2,...., x = 4n2 - 4n} n {x - 1, x - 2, x - 3, x - 5}. There is , however, an exception for the case of n = 8. For a pair of 3n £ 3n latin squares with holes of size 3 to have k entries in common outside of the holes k E {0, 1, 2,...., x = 9n2 - 9n} n {x - 1, x - 2, x - 3, x - 5}.