Statistics and Data Science Seminar
Rita Saha Ray
Stat-Math Division, Indian Statistical Institute
Critical Sets in Mutually Orthogonal Latin Squares
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.
Wednesday November 9, 2005 at 3:30 PM in SEO 512