We prove that the number of 01-fillings of a given stack polyomino (a polyomino with justified rows whose lengths form a unimodal sequence) with at most one 1 per column which do not contain a fixed-size northeast chain and a fixed-size southeast chain, depends only on the set of row lengths of the polyomino. The proof is via a bijection between fillings of stack polyominoes which differ only in the position of one row and uses the Hecke insertion algorithm by Buch, Kresch, Shimozono, Tamvakis, and Yong and the jeu de taquin for increasing tableaux of Thomas and Yong. Moreover, our bijection gives another proof of the result by Chen, Guo, and Pang that the crossing number and the nesting number have a symmetric joint distribution over linked partitions.

我们证明给定堆栈多义胺（具有合理行的多义胺，其长度形成单峰序列的多义胺）的01填充数（每列最多1个）不包含固定大小的东北链和固定大小的东南链，仅取决于多米诺的行长度集。证明是通过堆叠多米诺骨料的填充物之间的双射来实现的，这些填充物仅在一行的位置上有所不同，并使用Buch，Kresch，Shimozono，Tamvakis和Yong的Hecke插入算法以及jeu de taquin来提高Thomas和Yong的平衡感。此外，我们的双射也证明了Chen，Guo和Pang的结果，即交叉数和嵌套数在链接的分区上具有对称的联合分布。