Rita Saha Ray : Critical Sets in Mutually Orthogonal Latin Squares

Posted by , part of the Statistics and Data Science Seminar.

At

Nov. 9, 2005, 3:30 p.m.

In

SEO 512

Abstract

A critical set consists of the minimum information needed to recreate a combinatorial structure uniquely. To date, very few results on critical sets for a set of Mutually Orthogonal Latin Squares [MOLS] are known. In the present talk, we consider k Mutually Orthogonal Cyclic Latin Squares of order n, n odd, and obtain bounds on the possible sizes of the minimal critical sets. For n = 7, we consider a complete set of MOLS and exhibit a minimal critical set, improving upon the bound reported in Keedwell (1997). The problem is also addressed for a pair of MOLS of odd order n, n ≥ 9. Critical sets achieving the proposed bound are obtained for n = 9 and 15. (This is a joint work with Avishek Adhikari and Jennifer Seberry)

Tea will be provided at 3:15pm.