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pro vyhledávání: '"05A19, 11B75"'
Autor:
Uncu, Ali Kemal
In this paper we refine a weighted partition identity of Alladi. We write explicit formulas of generating functions for the number of partitions grouped with respect to a partition statistic other than the norm. We tie our weighted results and the di
Externí odkaz:
http://arxiv.org/abs/1603.00399
Publikováno v:
Journal of Combinatorics 9 (2018), no. 2, 221-232
For a given integer $d\ge 1$, we consider $\binom{n+d-1}{d}$-color compositions of a positive integer $\nu$ for which each part of size $n$ admits $\binom{n+d-1}{d}$ colors. We give explicit formulas for the enumeration of such compositions, generali
Externí odkaz:
http://arxiv.org/abs/1601.01595
Autor:
Komatsu, Takao
We define $q$-poly-Bernoulli polynomials $B_{n,\rho,q}^{(k)}(z)$ with a parameter $\rho$, $q$-poly-Cauchy polynomials of the first kind $c_{n,\rho,q}^{(k)}(z)$ and of the second kind $\widehat c_{n,\rho,q}^{(k)}(z)$ with a parameter $\rho$ by Jackson
Externí odkaz:
http://arxiv.org/abs/1503.08394
Autor:
Guo, Bai-Ni, Qi, Feng
Publikováno v:
Online Journal of Analytic Combinatorics 10 (2015), 5 pp
In the paper, utilizing respectively the induction, a generating function of the Lah numbers, the Chu-Vandermonde summation formula, an inversion formula, the Gauss hypergeometric series, and two generating functions of the Stirling numbers of the fi
Externí odkaz:
http://arxiv.org/abs/1402.2035
Autor:
Sun, Zhi-Wei, Zhao, Li-Lu
Publikováno v:
Colloq. Math. 130(2013), 67-78
For $k=1,2,\ldots$ let $H_k$ denote the harmonic number $\sum_{j=1}^k 1/j$. In this paper we establish some new congruences involving harmonic numbers. For example, we show that for any prime $p>3$ we have $$\sum_{k=1}^{p-1}\frac{H_k}{k2^k}\equiv\fra
Externí odkaz:
http://arxiv.org/abs/0911.4433
Autor:
Marc-Antoine Coppo
Publikováno v:
Results in Mathematics
Results in Mathematics, Springer Verlag, 2021, 76, pp.10. ⟨10.1007/s00025-021-01497-0⟩
Results in Mathematics, Springer Verlag, 2021, 76, pp.10. ⟨10.1007/s00025-021-01497-0⟩
Article paru dans Results in Mathematics (Springer).; International audience; In this article, we present a class of identities linking together Cauchy numbers, the special values of the Riemann zeta function and its derivative, and a generalization
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::960439e081b83687ad2ad4abb9bc1e1a
https://hal.univ-cotedazur.fr/hal-03131735
https://hal.univ-cotedazur.fr/hal-03131735
Publikováno v:
Journal of Combinatorics. 9:221-232
For a given integer $d\ge 1$, we consider $\binom{n+d-1}{d}$-color compositions of a positive integer $\nu$ for which each part of size $n$ admits $\binom{n+d-1}{d}$ colors. We give explicit formulas for the enumeration of such compositions, generali
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::09662df335961d7c04105ff0fc8eb54c
https://doi.org/10.4310/joc.2018.v9.n2.a1
https://doi.org/10.4310/joc.2018.v9.n2.a1
Autor:
Bai-Ni Guo, Feng Qi
Publikováno v:
Scopus-Elsevier
Web of Science
Web of Science
In the paper, utilizing respectively the induction, a generating function of the Lah numbers, the Chu-Vandermonde summation formula, an inversion formula, the Gauss hypergeometric series, and two generating functions of the Stirling numbers of the fi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f30f8fb78d29f2637872dab47411a515