On the Number of Even and Odd Latin Squares of Orderp+1
On the Number of Even and Odd Latin Squares of Orderp+1
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关于Orderp 1 的偶数和奇数拉丁方的个数
DOI：
10.1006/aima.1997.1623
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发表时间：
1997
影响因子：
1.7
通讯作者：
Arthur A. Drisko
中科院分区：
文献类型：
--
作者：
Arthur A. Drisko
本文证明了给定一个奇素数p，p +1阶的偶数拉丁方的个数不等于p +1阶的奇数拉丁方的个数。这一结果是一个特殊的情况下猜想的阿隆和Tarsi和各种其他组合问题的影响，包括prostitutures的罗塔和Dinitz。证明计数偶数和奇数拉丁方modulop3。这种计数使用了Zp的同位素、循环新域和正形的性质。
Abstract It is shown that given an odd primep, the number of even latin squares of orderp+1 is not equal to the number of odd latin squares of orderp+1. This result is a special case of a conjecture of Alon and Tarsi and has implications for various other combinatorial problems, including conjectures of Rota and Dinitz. The proof counts even and odd latin squares modulop3. This counting uses properties of isotopisms, cyclic neofields, and orthomorphisms of Z p.