Symmetrized poly-Bernoulli numbers and combinatorics

TL;DR

This paper explores the combinatorial properties of symmetrized poly-Bernoulli numbers, establishing a new relation with Dumont-Foata polynomials, thus advancing understanding of their combinatorial significance.

Contribution

It introduces a novel combinatorial relation between symmetrized poly-Bernoulli numbers and Dumont-Foata polynomials, enriching the combinatorial interpretation of these numbers.

Findings

Established a new relation between symmetrized poly-Bernoulli numbers and Dumont-Foata polynomials.

Provided combinatorial insights into negative index poly-Bernoulli numbers.

Enhanced understanding of the combinatorial structure of poly-Bernoulli numbers.

Abstract

Poly-Bernoulli numbers are one of generalizations of the classical Bernoulli numbers. Since a negative index poly-Bernoulli number is an integer, it is an interesting problem to study this number from combinatorial viewpoint. In this short article, we give a new combinatorial relation between symmetrized poly-Bernoulli numbers and the Dumont-Foata polynomials.