### Abstract

The sign of a Latin square is -1 if it has an odd number of rows and columns that are odd permutations; otherwise, it is +1. Let L-n(E) and L-n(O) be, respectively, the number of Latin squares of order n with sign +1 and -1. The Alon-Tarsi conjecture asserts that L-n(E)not equal L-n(O) when n is even. Drisko showed that L-p+1(E) not equivalent to L-p+1(O) (mod p(3)) for prime p >= 3 and asked if similar congruences hold for orders of the form p(k) + 1, p + 3, or pq + 1. In this article we show that if t

Original language | English |
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Pages (from-to) | 1 - 24 |

Number of pages | 24 |

Journal | Nagoya Mathematical Journal |

Volume | 205 |

DOIs | |

Publication status | Published - 2012 |

## Cite this

Stones, D., & Wanless, I. M. (2012). How not to prove the Alon-Tarsi conjecture.

*Nagoya Mathematical Journal*,*205*, 1 - 24. https://doi.org/10.1215/00277630-1543769