14 citations · 21 across the 11 of their papers we have counts for
14 papers
Remarkable relations between the central binomial series, Eulerian polynomials, and poly-Bernoulli numbers
Beáta Bényi, Toshiki Matsusaka
The central binomial series at negative integers are expressed as a linear combination of values of certain two polynomials. We show that one of the polynomials is a special value…
Weak ascent sequences and related combinatorial structures
Beáta Bényi, Anders Claesson, Mark Dukes
In this paper we introduce {\em weak ascent sequences}, a class of number sequences that properly contains ascent sequences. We show how these sequences uniquely encode each of the…
Combinatorial aspects of poly-Bernoulli polynomials and poly-Euler numbers
Beáta Bényi, Toshiki Matsusaka
In this article, we introduce combinatorial models for poly-Bernoulli polynomials and poly-Euler numbers of both kinds. As their applications, we provide combinatorial proofs of so…
Poly-Cauchy numbers -- the combinatorics behind
Beáta Bényi, José Luis Ramírez
We introduce poly-Cauchy permutations that are enumerated by the poly-Cauchy numbers. We provide combinatorial proofs for several identities involving poly-Cauchy numbers and some…
Toppling on permutations with an extra chip
Arvind Ayyer, Beáta Bényi
The study of toppling on permutations with an extra labeled chip was initiated by the first author with D. Hathcock and P. Tetali (arXiv:2010.11236), where the extra chip was added…
Combinatorial proof of an identity on Genocchi numbers
Beáta Bényi, Matthieu Josuat-Vergès
In this note we present a combinatorial proof of an identity involving poly-Bernoulli numbers and Genocchi numbers. We introduce the combinatorial objects, barred Callan sequen…
On the combinatorics of symmetrized poly-Bernoulli numbers
Beáta Bényi, Toshiki Matsusaka
In this paper we introduce three combinatorial models for symmetrized poly-Bernoulli numbers. Based on our models we derive generalizations of some identities for poly-Bernoulli nu…
Lonesum and -free - fillings of Ferrers shapes
Gábor V. Nagy, Beáta Bényi
We show that -free fillings and lonesum fillings of Ferrers shapes are equinumerous by applying a previously defined bijection on matrices for this more general case and by cons…
On -poly-Bernoulli numbers arising from combinatorial interpretations
Beáta Bényi, José Luis Ramírez
In this paper we present several natural -analogues of the poly-Bernoulli numbers arising in combinatorial contexts. We also recall some relating analytical results and ask for…
A Combinatorial Analysis Of Higher Order Generalised Geometric Polynomials: A Generalisation Of Barred Preferential Arrangements
Sithembele Nkonkobe, Beáta Bényi, Roberto B. Corcino +1
A barred preferential arrangement is a preferential arrangement, onto which in-between the blocks of the preferential arrangement a number of identical bars are inserted. We offer…
Generalised Barred Preferential Arrangements
Sithembele Nkonkobe, Venkat Murali, Béata Bényi
A barred preferential arrangement is a preferential arrangement onto which a number of identical bars are inserted in between the blocks of the preferential arrangement. In this st…
Mixed coloured permutations
Beáta Bényi, Daniel Yaqubi
In this paper we introduce mixed coloured permutation, permutations with certain coloured cycles, and study the enumerative properties of these combinatorial objects. We derive the…
Combinatorial properties of poly-Bernoulli relatives
Beáta Bényi, Péter Hajnal
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 varia…
Combinatorics of poly-Bernoulli numbers
Beáta Bényi, Peter Hajnal
The poly-Bernoulli numbers --- a natural generalization of classical Bernoulli numbers () --- were introduced by Kaneko in 1997. When…