论文标题
戴森的曲柄和整数分区的mex
Dyson's Crank and the Mex of Integer Partitions
论文作者
论文摘要
安德鲁斯（Andrews）和纽曼（Newman）最近介绍了一个分区的MEX概念，这是最小的积极整数，不是一部分。但是，至少从2011年开始使用该概念，并与Frobenius符号有联系。最近，MEX的奇偶校验与戴森（Dyson）在1944年命名的曲柄统计量有关。在本说明中，我们通过证明许多自然将这些分区统计的属性证明了许多属性，从而扩展和加强了曲柄和MEX之间的联系（以及MEX的新概括）。
Andrews and Newman have recently introduced the notion of the mex of a partition, the smallest positive integer that is not a part. The concept has been used since at least 2011, though, with connections to Frobenius symbols. Recently the parity of the mex has been associated to the crank statistic named by Dyson in 1944. In this note, we extend and strengthen the connection between the crank and mex (along with a new generaliztion of the mex) by proving a number of properties that naturally relate these partition statistics.
