Title: The combinatorics of identities involving three kinds of counting numbers

Authors: Lun Lv; Sabrina X.M. Pang

Addresses: School of Sciences, Hebei University of Science and Technology, Shijiazhuang, Hebei, 050018, China. ' College of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang, Hebei, 050061, China

Abstract: This paper answers the problem recently proposed by Hsu on identities involving the binomial coefficients and the two kinds of Stirling numbers. We explain Hsu's identities based on the well-known combinatorial interpretations of the two kinds of Stirling numbers.

Keywords: permutation; partition; Stirling numbers; combinatorial identity; counting number; modelling; combinatorics; binomial coefficients.

DOI: 10.1504/IJMIC.2012.047741

International Journal of Modelling, Identification and Control, 2012 Vol.16 No.3, pp.291 - 296

Published online: 17 Dec 2014 *

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