彩色洗牌兼容，哈达玛产品，并问zeta功能

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-05-05 DOI:10.1112/blms.70081

Angela Carnevale, Vassilis Dionyssis Moustakas, Tobias Rossmann

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引用次数: 0

摘要

给出了一类有理生成函数的哈达玛积组合公式的显式计算方法。后者在研究矩阵的模的直接和的所谓的问ζ函数或幂零群的直接积的类和轨道计数的ζ函数时自然出现。我们的方法依赖于有色排列统计量和有色拟对称函数的洗牌兼容性，扩展了Gessel和Zhuang的最新工作。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Coloured shuffle compatibility, Hadamard products, and ask zeta functions

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Coloured shuffle compatibility, Hadamard products, and ask zeta functions

We devise an explicit method for computing combinatorial formulae for Hadamard products of certain rational generating functions. The latter arise naturally when studying so-called ask zeta functions of direct sums of modules of matrices or class- and orbit-counting zeta functions of direct products of nilpotent groups. Our method relies on shuffle compatibility of coloured permutation statistics and coloured quasisymmetric functions, extending recent work of Gessel and Zhuang.

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