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’AntonaSecondo
;
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.Pubblicazioni consigliate
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