Séminaire Lotharingien de Combinatoire, 91B.56 (2024), 12 pp.
Angela Carnevale, Vassilis Dionyssis Moustakas and Tobias Rossmann
From Coloured Permutations to Hadamard Products and Zeta Functions
Abstract.
We devise a constructive method for computing
explicit 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 groups.
Our method relies on shuffle compatibility of coloured permutation
statistics and coloured quasisymmetric functions, extending recent work of
Gessel and Zhuang.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
The following versions are available: