Combinatorics of poly-Bernoulli numbers
| Autor: | Péter Hajnal, Beáta Bényi |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Studia Scientiarum Mathematicarum Hungarica. 52:537-558 |
| ISSN: | 1588-2896 0081-6906 |
| DOI: | 10.1556/012.2015.52.4.1325 |
| Popis: | 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 Comment: 20 pages, to appear in Studia Scientiarum Mathematicarum Hungarica |
| Databáze: | OpenAIRE |
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