论文标题
计数具有钩长的决定因素的POSET的线性扩展
Counting linear extensions of posets with determinants of hook lengths
论文作者
论文摘要
我们介绍了一类Posets，其中包括功能区POSET（偏斜形状）和$ d $ complete posets，以便它们的线性扩展数量由矩阵的矩阵的决定因素给出，其条目是挂钩长度的产物。我们还根据主要索引和反转统计数据提供了该决定性公式的$ Q $ - 分析。 As applications, we give families of tree posets whose numbers of linear extensions are given by generalizations of Euler numbers, we draw relations to Naruse-Okada's positive formulas for the number of linear extensions of skew $d$-complete posets, and we give polynomiality results analogous to those of descent polynomials by Diaz-López, Harris, Insko, Omar, and Sagan.
We introduce a class of posets, which includes both ribbon posets (skew shapes) and $d$-complete posets, such that their number of linear extensions is given by a determinant of a matrix whose entries are products of hook lengths. We also give $q$-analogues of this determinantal formula in terms of the major index and inversion statistics. As applications, we give families of tree posets whose numbers of linear extensions are given by generalizations of Euler numbers, we draw relations to Naruse-Okada's positive formulas for the number of linear extensions of skew $d$-complete posets, and we give polynomiality results analogous to those of descent polynomials by Diaz-López, Harris, Insko, Omar, and Sagan.
