On the number of even latin squares of even order

TL;DR

This paper discusses the Alon-Tarsi conjecture related to counting even Latin squares of even order and introduces a parity-switching map with an example.

Contribution

It presents a new map that switches the parity of Latin squares under specific conditions, advancing understanding of their enumeration.

Findings

The map demonstrates a method to relate even and odd Latin squares.

Provides an example illustrating the parity switch.

Contributes to the study of the Alon-Tarsi conjecture.

Abstract

We recall the Alon-Tarsi conjecture on the number of even latin squares. We introduce a map which switches the parity of a latin square under certain requirements. An example is included.