Embedding partial Latin squares into sets of MOLS
SPEAKER: E. Sule Yazici, Koc University, Turkey.
Date: Wednesday 10th April
Time: 3:00pm–4:00pm (Talk & Q/A)
Venue: Building 8 Level 9 Room 66 (AGR) RMIT City campus
The seminar will be followed by snacks and drinks
All students, staff and visitors are welcome
ABSTRACT: In 1960 Evans proved that a partial Latin square of order n can always be embedded in some Latin square of order t for every t≥2n. In the same paper Evans asked if a pair of finite partial Latin squares which are orthogonal can be embedded in a pair of finite orthogonal Latin squares. It is known, that a pair of orthogonal Latin squares of order n can be embedded in a pair of orthogonal Latin squares of order t if t ≥3n, the bound of 3n being best possible. Jenkins considered embedding a single partial Latin square in a Latin square which has an orthogonal mate. His embedding was of order t2.
We showed that any partial Latin square of order n can be embedded in a Latin square of order at most 16n2 which has at least 2n-1 mutually orthogonal mates. We also showed that a pair of (partial) orthogonal Latin squares of order n can be embedded into a set of t mutually orthogonal Latin squares of order a polynomial with respect to n for any t≥2. Furthermore the constructions we provided, give a set of 9 MOLS(576).
Joint Work with Diane Donovan (UQ) and Mike Grannell (Open University UK)
BIOGRAPHY: Associate Professor Sule Yazuci is with the Department of Mathematics at Koc University in Turkey. Her research focuses on combinatorial designs.