卡勒多项式

Pub Date : 2024-07-24 DOI:10.1016/j.disc.2024.114177

Giulio Cerbai, Anders Claesson

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引用次数: 0

摘要

欧拉多项式根据降序的数量枚举排列。我们开始研究 Cayley 排列的降序多项式，我们称之为 Caylerian 多项式。通过将 Caylerian 多项式与 Burge 词和 Burge 矩阵联系起来，一些经典结果得到了推广。两边欧拉多项式的γ非负性用伯格结构重新表述。最后，证明了具有规定上升集的 Cayley 置换可以用具有固定行和的 Burge 矩阵来计算。

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Caylerian polynomials

The Eulerian polynomials enumerate permutations according to their number of descents. We initiate the study of descent polynomials over Cayley permutations, which we call Caylerian polynomials. Some classical results are generalized by linking Caylerian polynomials to Burge words and Burge matrices. The γ-nonnegativity of the two-sided Eulerian polynomials is reformulated in terms of Burge structures. Finally, Cayley permutations with a prescribed ascent set are shown to be counted by Burge matrices with fixed row sums.

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