论文标题
交替符号梯形的四倍精制枚举
A Fourfold Refined Enumeration of Alternating Sign Trapezoids
论文作者
论文摘要
最近引入了交替的标志梯形作为交替的符号三角形的概括。菲舍尔（Fischer）建立了交替符号梯形的三倍精制枚举，并提供了三个有关柱严格移动平面分区的统计数据，具有相同的关节分布。在本文中，我们能够在这些结果中添加一对新的统计信息。更确切地说，我们考虑交替的符号梯形上的$ -1 $ s的数量，并在列引入相应的统计量严格移动的平面分区，该平面分区具有相同的分布。更普遍地，我们表明，两个关于交替符号梯形的四个四元组的联合分布分别分别与严格移动的平面分区相吻合。此外，我们为交替的符号梯形的$ 2 $增强提供了封闭式表达式。
Alternating sign trapezoids have recently been introduced as a generalisation of alternating sign triangles. Fischer established a threefold refined enumeration of alternating sign trapezoids and provided three statistics on column strict shifted plane partitions with the same joint distribution. In this paper, we are able to add a new pair of statistics to these results. More precisely, we consider the number of $-1$s on alternating sign trapezoids and introduce a corresponding statistic on column strict shifted plane partitions that has the same distribution. More generally, we show that the joint distributions of the two quadruples of statistics on alternating sign trapezoids and column strict shifted plane partitions, respectively, coincide. In addition, we provide a closed-form expression for the $2$-enumeration of alternating sign trapezoids.
