In a series of papers, P. Blasiak et al. developed a wide-ranging generalization of Bell numbers (and of Stirling numbers of the second kind) that is relevant to the so-called boson normal ordering problem. They provided a recurrence and, more recently, also offered a (fairly complex) combinatorial interpretation of these numbers. We show that by restricting the numbers somewhat (but still widely generalizing Bell and Stirling numbers), one can supply a much more natural combinatorial interpretation. In fact, we offer two different such interpretations, one in terms of graph colourings and another one in terms of certain labelled Eulerian digraphs.

A simple combinatorial interpretation of certain generalized Bell and Stirling numbers / P. Codara, O.M. D’Antona, P. Hell. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - 318:1(2014 Mar 06), pp. 53-57. [10.1016/j.disc.2013.11.010]

A simple combinatorial interpretation of certain generalized Bell and Stirling numbers

P. Codara
;
O.M. D’Antona
Secondo
;
2014

Abstract

In a series of papers, P. Blasiak et al. developed a wide-ranging generalization of Bell numbers (and of Stirling numbers of the second kind) that is relevant to the so-called boson normal ordering problem. They provided a recurrence and, more recently, also offered a (fairly complex) combinatorial interpretation of these numbers. We show that by restricting the numbers somewhat (but still widely generalizing Bell and Stirling numbers), one can supply a much more natural combinatorial interpretation. In fact, we offer two different such interpretations, one in terms of graph colourings and another one in terms of certain labelled Eulerian digraphs.
Generalized Bell number; Generalized Stirling number; Labelled Eulerian graph; Graph colouring
Settore INF/01 - Informatica
Settore MAT/03 - Geometria
6-mar-2014
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/228268
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