| Autor: |
Méndez Miguel A., Ramírez José L. |
| Jazyk: |
angličtina |
| Rok vydání: |
2019 |
| Předmět: |
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| Zdroj: |
Acta Universitatis Sapientiae: Mathematica, Vol 11, Iss 2, Pp 387-418 (2019) |
| Druh dokumentu: |
article |
| ISSN: |
2066-7752 |
| DOI: |
10.2478/ausm-2019-0029 |
| Popis: |
In the present article we introduce two new combinatorial interpretations of the r-Whitney numbers of the second kind obtained from the combinatorics of the differential operators associated to the grammar G := {y → yxm, x → x}. By specializing m = 1 we obtain also a new combinatorial interpretation of the r-Stirling numbers of the second kind. Again, by specializing to the case r = 0 we introduce a new generalization of the Stirling number of the second kind and through them a binomial type family of polynomials that generalizes Touchard’s polynomials. Moreover, we recover several known identities involving the r-Dowling polynomials and the r-Whitney numbers using the combinatorial differential calculus. We construct a family of posets that generalize the classical Dowling lattices. The r-Withney numbers of the first kind are obtained as the sum of the Möbius function over elements of a given rank. Finally, we prove that the r-Dowling polynomials are a Sheffer family relative to the generalized Touchard binomial family, study their umbral inverses, and introduce [m]-Stirling numbers of the first kind. From the relation between umbral calculus and the Riordan matrices we give several new combinatorial identities |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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