2019
DOI: 10.2478/ausm-2019-0029
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A new approach to the r-Whitney numbers by using combinatorial differential calculus

Abstract: 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 polynomi… Show more

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Cited by 2 publications
(1 citation statement)
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“…The order so defined is isomorphic to the classical Dowling lattice [Dow73]. We are going to generalize this construction to a poset Q n ,r (G ) depending on a second parameter r and whose Withney numbers of the first and second kind coincide with those defined in [MR17].…”
Section: Examplesmentioning
confidence: 99%
“…The order so defined is isomorphic to the classical Dowling lattice [Dow73]. We are going to generalize this construction to a poset Q n ,r (G ) depending on a second parameter r and whose Withney numbers of the first and second kind coincide with those defined in [MR17].…”
Section: Examplesmentioning
confidence: 99%