A simple combinatorial interpretation of certain generalized Bell and Stirling numbers

作者：Codara Pietro^*; D'Antona Ottavio M; Hell Pavol

来源：Discrete Mathematics, 2014, 318: 53-57.

DOI：10.1016/j.disc.2013.11.010

• Generalized Bell number
• Generalized Stirling number
• Labelled Eulerian graph
• Graph colouring

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.

• 出版日期2014-3-6