Bijective enumerations for symmetrized poly-Bernoulli polynomials

TL;DR

This paper establishes bijections between combinatorial objects related to symmetrized poly-Bernoulli polynomials and proves their equivalence with various combinatorial polynomials, enhancing understanding of their structure.

Contribution

It introduces bijections between two combinatorial interpretations and shows their equivalence with multiple combinatorial polynomials for symmetrized poly-Bernoulli polynomials.

Findings

Bijections between combinatorial objects are constructed.

Various combinatorial polynomials are shown to coincide with symmetrized poly-Bernoulli polynomials.

Enhanced understanding of the combinatorial structure of symmetrized poly-Bernoulli polynomials.

Abstract

Recently, B\'{e}nyi and the second author introduced two combinatorial interpretations for symmetrized poly-Bernoulli polynomials. In the present study, we construct bijections between these combinatorial objects. We also define various combinatorial polynomials and prove that all of these polynomials coincide with symmetrized poly-Bernoulli polynomials.