On $q$-poly-Bernoulli numbers arising from combinatorial interpretations

TL;DR

This paper introduces new $q$-analogues of poly-Bernoulli numbers based on combinatorial interpretations, reviews related analytical results, and explores potential combinatorial meanings.

Contribution

It presents several natural $q$-analogues of poly-Bernoulli numbers and discusses their combinatorial and analytical aspects, proposing new directions for interpretation.

Findings

Introduction of new $q$-analogues of poly-Bernoulli numbers

Connection between combinatorial contexts and analytical results

Open questions on combinatorial interpretations

Abstract

In this paper we present several natural $q$-analogues of the poly-Bernoulli numbers arising in combinatorial contexts. We also recall some relating analytical results and ask for combinatorial interpretations.