arXiv subjects

Beáta Bényi

Publications and source records attributed to Beáta Bényi.

21 records · Page 2Linked to original sources

arXiv2017

Bijective enumerations of $Γ$-free 0-1 matrices

We construct a new bijection between the set of $n\times k$ $0$-$1$ matrices with no three $1$'s forming a $Γ$ configuration and the set of $(n,k)$-Callan sequences, a simple structure counted by poly-Bernoulli numbers. We give two applications of this result: We derive the generating function of $Γ$-free matrices, and we give a new bijective proof for an elegant result of Aval et al. that states that the number of complete non-ambiguous forests with $n$ leaves is equal to the number of pairs of permutations of $\{1,\dots,n\}$ with no common rise.

math.CO↗

arXiv2016

Combinatorial properties of poly-Bernoulli relatives

In this note we augment the poly-Bernoulli family with two new combinatorial objects. We derive formulas for the relatives of the poly-Bernoulli numbers using the appropriate variations of combinatorial interpretations. Our goal is to show connections between the different areas where poly-Bernoulli numbers and their relatives appear and give examples how the combinatorial methods can be used for deriving formulas between integer arrays.

math.CO↗

arXiv2015

Combinatorics of poly-Bernoulli numbers

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 $k$ is negative then ${\mathbb B}_n^{(k)}$ is a nonnegative number. Brewbaker was the first to give combinatorial interpretation of these numbers. He proved that ${\mathbb B}_n^{(-k)}$ counts the so called lonesum $0\text{-}1$ matrices of size $n\times k$. Several other interpretations were pointed out. We survey these and give new ones. Our new interpretation, for example, gives a transparent, combinatorial explanation of Kaneko's recursive formula for poly-Bernoulli numbers

math.CO↗