On extensions of the Alon-Tarsi Latin square conjecture (Q1953309)

Summary: Expressions involving the product of the permanent with the \((n-1)\)st power of the determinant of a matrix of indeterminates, and of \((0,1)\)-matrices, are shown to be related to an extension to odd dimensions of the Alon-Tarsi Latin Square Conjecture, first stated by Zappa. These yield an alternative proof of a theorem of Drisko, stating that the extended conjecture holds for Latin squares of odd prime order. An identity involving an alternating sum of permanents of \((0,1)\)-matrices is obtained.