Partially strict shifted plane partitions
Partially strict shifted plane partitions
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部分严格的平移平面分区
DOI：
10.1016/0097-3165(90)90025-r
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发表时间：
1990
期刊：
影响因子：
--
通讯作者：
S. Okada
中科院分区：
文献类型：
--
作者：
S. Okada
对于正整数的互补子集对（A，B），（A，B）-部分严格移位平面划分是移位平面划分σ=（aij）i j（aij ai，j+1和aij ai+ 1，j）使得（i）对于任意m A，映射在每一行至多出现一次，（ii）对于任意m B，映射在每一列至多出现一次.本文用格路方法给出了它们的生成函数。作为这个生成函数的一个应用，我们可以得到一个生成函数，用于行严格（分别）。列严格）移位平面划分，这是一个决定性的公式，在初等（分别）。完全）对称多项式。另一个应用是导出单调三角形的加权生成函数。
For a pair (A,B) of complementary subsets of positive integers, an(A, B)-partially strict shifted plane partitionis a shifted plane partitionσ= (aij)i⩽j(aij⩾ai,j+1andaij⩾ai+ 1,j) such that (i) for anymϵA,mappears at most once in each row, and (ii) for anymϵB,mappears at most once in each column. In this paper we give a generaging function for them by using a “lattice path” method. As one application of this generating function, we can obtain a generating function for row-strict (resp. column-strict) shifted plane partitions, which is a determininantal formula in terms of elementary (resp. complete) symmetric polynomials. Another application is to derive a weighted generating function for monotone triangles.