On completing three cyclic transversals to a latin square

Abstract

Let $P$ be a partial latin square of prime order $p>7$ consisting of three cyclically generated transversals. Specifically, let $P$ be a partial latin square of the form: \[ P=\{(i,c+i,s+i),(i,c'+i,s'+i),(i,c''+i,s''+i)\mid 0 \leq i< p\} \] for some distinct $c,c^{\prime },c^{\prime \prime }$ and some distinct $s,s^{\prime },s^{\prime \prime }$. In this paper we show that any such $P$ completes to a latin square which is diagonally cyclic.

13 pages, SAGE source code