On extensions of the Alon-Tarsi Latin Square conjecture

Abstract

Expressions involving the product of the permanent with the (n-1)th power of the determinant of a matrix of indeterminates, and of (0,1)-matrices, are shown to be related to two conjectures that extend the Alon-Tarsi Latin square conjecture to odd dimensions. An identity involving an alternating sum of permanents of (0,1)-matrices is obtained.