**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* t*^{2}.

We showed that any partial Latin square of order* n* can be embedded in a Latin square of order at most *16n ^{2} *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)

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**BIOGRAPHY: **Associate Professor Sule Yazuci is with the Department of Mathematics at Koc University in Turkey. Her research focuses on combinatorial designs.

http://home.ku.edu.tr/~eyazici/