Generalized Stirling numbers and hyper-sums of powers of binomials coefficients
type: Item
instance of: scholarly article
title: Generalized Stirling numbers and hyper-sums of powers of binomials coefficients
zbMATH Open document ID: 1308.11020
author: Claudio de J. Pita Ruiz V.
published in: The Electronic Journal of Combinatorics
publication date: 2014-09-04T00:00:00Z
full work available at URL: v21i1p10
review text: Summary: We work with a generalization of Stirling numbers of the second kind related to the boson normal ordering problem [\textit{P. Blasiak} et al., Am. J. Phys. 75, No. 7, 639--646 (2007; Zbl 1219.81165)]. We show that these numbers appear as part of the coefficients of expressions in which certain sequences of products of binomials, together with their partial sums, are written as linear combinations of some other binomials. We show that the number arrays formed by these coefficients can be seen as natural generalizations of Pascal and Lucas triangles, since many of the known properties on rows, columns, falling diagonals and rising diagonals in Pascal and Lucas triangles, are also valid (some natural generalizations of them) in the arrays considered in this work. We also show that certain closed formulas for hyper-sums of powers of binomial coefficients appear in a natural way in these arrays.
Mathematics Subject Classification ID: 11B65
Mathematics Subject Classification ID: 05A10
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 11B73
zbMATH DE Number: 6340108
zbMATH Keywords: Stirling numbers
zbMATH Keywords: sums of powers of binomials coefficients
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6340108