Work

Coloured shuffle compatibility, Hadamard products, and ask zeta functions

Year: 2025

Type: article

Abstract: 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.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70081

Authors: Angela Carnevale, Vassilis Dionyssis Moustakas, Tobias Rossmann

Institutions: Ollscoil na Gaillimhe – University of Galway, University of Pisa

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: University of Galway, College of Science and Engineering, University of Minnesota