On the number of transversals in a class of Latin squares

Donovan, Diane M. and Grannell, Mike J. (2018). On the number of transversals in a class of Latin squares. Discrete Applied Mathematics, 235 pp. 202–205.

DOI: https://doi.org/10.1016/j.dam.2017.08.021

Abstract

Denote by $\mathcal{A}_p^k$ the Latin square of order $n=p^k$ formed by the Cayley table of the additive group $(\mathbb{Z}_p^k,+)$, where $p$ is an odd prime and $k$ is a positive integer. It is shown that for each $p$ there exists $Q>0$ such that for all sufficiently large $k$, the number of transversals in $\mathcal{A}_p^k$ exceeds $(nQ)^{\frac{n}{p(p-1)}}$.

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