移动平面分拆的计数

Enumeration of shifted plane partitions

建立了正整数ｎ的列严格平面分拆全体组成的集合和它的移动平面分拆全体组成的集合之间的一一对应，以及列严格行长为偶数的平面分拆组成的集合和主对角线上的元素为偶数的非负整数对称矩阵组成的集合之间的一一对应。在此基础上给出移动平面分拆及一类特殊的移动平面分拆的计数。

The bijection between the set of all column strict plane partitions of a positive integer n and the set of all shifted plane partitions of the n, and the bijection between the set of all column strict plane partitions with the lengths of rows being even and the set of all symmetric non- negative integer matrices with main diagonal entries being even are established. Therefore, the enumerations of shifted plane partitions and a special class of shifted plane partitions are given.