论文标题
非负曲柄的概括 - odd mex身份的概念证明
A bijective proof of a generalization of the non-negative crank--odd mex identity
论文作者
论文摘要
安德鲁斯（Newman）和霍普金斯（Hopkins）的最新作品 - 销售商传播了两个分区统计数据，即曲柄和MEX之间的有趣关系。他们指出，对于一个积极的整数$ n $，与非负式曲柄的$ n $相同，与$ n $的分区相同。在本文中，我们给出了霍普金斯，卖方和斯坦顿提供的这种身份的概括的徒证明。我们的方法使用了Durfee分解的替代定义，霍普金斯，卖家和YEE最近研究了其与曲柄的组合链接。
Recent works of Andrews--Newman and Hopkins--Sellers unveil an interesting relation between two partition statistics, the crank and the mex. They state that, for a positive integer $n$, there are as many partitions of $n$ with non-negative crank as partitions of $n$ with odd mex. In this paper, we give a bijective proof of a generalization of this identity provided by Hopkins, Sellers, and Stanton. Our method uses an alternative definition of the Durfee decomposition, whose combinatorial link to the crank was recently studied by Hopkins, Sellers, and Yee.
