On the number of transversals in latin squares

TL;DR

This paper establishes a lower bound on the maximum number of transversals in Latin squares of order n, showing it grows at least as fast as a function involving n and its logarithm.

Contribution

It provides a new asymptotic lower bound on the maximum number of transversals in Latin squares, advancing understanding of their combinatorial complexity.

Findings

Maximum number of transversals exceeds exp(n/6 * (ln n + O(1)))

Lower bound improves previous estimates on Latin square transversals

Highlights growth rate of transversals in large Latin squares

Abstract

The logarithm of the maximum number of transversals over all latin squares of order $n$ is greater than $\frac{n}{6}(\ln n+ O(1))$.