# Bijective enumerations for symmetrized poly-Bernoulli polynomials

@inproceedings{Hirose2021BijectiveEF, title={Bijective enumerations for symmetrized poly-Bernoulli polynomials}, author={M. Hirose and Toshiki Matsusaka and Ryutaro Sekigawa and Hyuga Yoshizaki}, year={2021} }

Recently, Bényi 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.

#### References

SHOWING 1-10 OF 19 REFERENCES

On the Combinatorics of Symmetrized Poly-Bernoulli Numbers

- Mathematics, Computer Science
- Electron. J. Comb.
- 2021

Three combinatorial models for symmetrized poly- Bernoulli numbers are introduced and generalizations of some identities for poly-BernoulliNumbers are derived. Expand

Symmetrized poly-Bernoulli numbers and combinatorics

- Mathematics
- 2020

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… Expand

On a duality formula for certain sums of values of poly-Bernoulli polynomials and its application

- Mathematics
- 2016

We prove a duality formula for certain sums of values of poly-Bernoulli polynomials which generalizes dualities for poly-Bernoulli numbers. We first compute two types of generating functions for… Expand

A combinatorial interpretation of the poly-Bernoulli numbers and two Fermat analogues.

- Mathematics
- 2008

We show that the number of (0, 1)-matrices with n rows and k columns uniquely reconstructable from their row and column sums is the poly-Bernoulli number B n . Combinatorial proofs for both the sieve… Expand

On Poly-Bernoulli numbers

- Mathematics
- 1997

In this chapter, we define and study a generalization of Bernoulli numbers referred to as poly-Bernoulli numbers, which is a different generalization than the generalized Bernoulli numbers introduced… Expand

The structure of alternative tableaux

- Computer Science, Mathematics
- J. Comb. Theory, Ser. A
- 2011

This paper exhibits a simple recursive structure for alternative tableaux, from which it can easily deduce a number of enumerative results and gives bijections between these tableaux and certain classes of labeled trees. Expand

The Excedance Set of a Permutation

- Mathematics, Computer Science
- Adv. Appl. Math.
- 2000

The excedance set of a permutation ?=?1?2···?n is the set of indices i for which ?ii. We give a formula for the number of permutations with a given excedance set and recursive formulas satisfied by… Expand

Explicit expressions for the extremal excedance set statistics

- Mathematics, Computer Science
- Eur. J. Comb.
- 2010

This work recast these explicit formulas for the number of permutations as LDU-decompositions of associated matrices and show that these matrices are totally non-negative. Expand

Combinatorics of poly-Bernoulli numbers

- Mathematics
- 2015

The ${\mathbb B}_n^{(k)}$ poly-Bernoulli numbers --- a natural generalization of classical Bernoulli numbers ($B_n={\mathbb B}_n^{(1)}$) --- were introduced by Kaneko in 1997. When the parameter $k$… Expand

RANK t ℋ-PRIMES IN QUANTUM MATRICES

- Mathematics
- 2003

ABSTRACT Let 𝕂 be a (commutative) field and consider a nonzero element q in 𝕂 that is not a root of unity. Goodearl and Lenagan (2002) have shown that the number of ℋ-primes in R = O q (ℳ n (𝕂))… Expand