On Extensions of the Alon-Tarsi Latin Square Conjecture

  • Daniel Kotlar
Keywords: Latin square, Alon-Tarsi Latin Square conjecture, Parity of a Latin square, adjacency matrix, permanent of (0, 1)-matrix


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.
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