Geodesic
On extensions of the Alon-Tarsi Latin square conjecture
Daniel Kotlar1
1Tel-Hai College
The electronic journal of combinatorics, Tome 19 (2012) no. 4
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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.
DOI : 10.37236/2269
Classification : 05B15, 05B20, 15A15
Mots-clés : Alon-Tarsi Latin square conjecture, parity of a Latin square, adjacency matrix, permanent of (0,1)-matrix

Daniel Kotlar  1

1 Tel-Hai College 
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Daniel Kotlar. On extensions of the Alon-Tarsi Latin square conjecture. The electronic journal of combinatorics, Tome 19 (2012) no. 4. doi: 10.37236/2269

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