# A polynomial embedding of pairs of orthogonal partial latin squares

Presented by:

Emine Şule Yazıcı, Koç University, Turkey
Date:

Tue 12 Aug, 3:00 pm - 4:00 pm
Venue:

Building 67, Room 442 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 raised the question as to whether a pair of finite partial latin squares which are orthogonal can be embedded in a pair of finite orthogonal latin squares. We show that a pair of orthogonal partial latin squares of order t can be embedded in a pair of orthogonal latin squares of order at most 16t^4 and all orders greater than or equal to 48t^4. This is the first polynomial embedding result of its kind.