A remark on the Alon Tarsi conjecture

Martin Loebl

Abstract

(joint work with Ron Aharoni) The sign of a latin square L of order n is the product of the 2n signs of all its rows and columns. L is called restricted if its first row and column is the identity permutation.

Alon-Tarsi conjecture: for each n even, the sum of the signs of the latin squares of order n is non-zero.

Wanless, Kotlar conjecture: for each n, the sum of the signs of the restricted latin squares of order n is non-zero.

We prove that these two conjectures are equivalent.