Combinatorics Seminar

Speaker: A J W Hilton, University of Reading and Queen Mary College University of London, UK

Abstract: We generalize Hall's Condition for a system of distinct representatives and apply it to obtain results about completing latin squares. A latinized square is a generalization of a latin square. We have a set v1,v2,.....,vn of positive integers and a positive integer p such that v1 + v2 + .......+vn = p^2 and 1 <= vi <=p.  A p x p array on symbols x1, x2, ......,xn such that each xi occurs vi times, and no xi occurs twice in any row or column is a (v1,v2,......,vn)-latinized square. We give some completion results for this type of square.