منابع مشابه
Set partition statistics and q-Fibonacci numbers
We consider the set partition statistics ls and rb introduced by Wachs and White and investigate their distribution over set partitions avoiding certain patterns. In particular, we consider those set partitions avoiding the pattern 13/2, Πn(13/2), and those avoiding both 13/2 and 123, Πn(13/2, 123). We show that the distribution over Πn(13/2) enumerates certain integer partitions, and the distr...
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To RICHARD RADO for his 65th birthday Q 1. Introduction The ordinary partition symbol invented by R. RADO and first introduced in [l] enables us to study systematically the possible generalizations of RAIXSEY'S theorem. denotes that the following statement is true. Let (S,-<) be an ordered set; tp S(-<) = ,z or let S be a set 1 S 1 = a if CL is an order type or z is a cardinal respectively. Let...
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We define a generalization of the Stirling numbers of the first and second kinds and develop a new rook theory model to give combinatorial interpretations to these numbers. These rook-theoretic interpretations are used to give a direct combinatorial proof that two associated matrices are inverses of each other. We also give combinatorial interpretations of the numbers in terms of certain collec...
متن کاملAsymptotics of several-partition Hurwitz numbers
We derive in this paper the asymptotics of several-partition Hurwitz numbers, relying on a theorem of Kazarian for the one-partition case and on an induction carried on by Zvonkine. Essentially, the asymptotics for several partitions is the same as the one-partition asymptotics obtained by concatenating the partitions. Résumé. Dans cet article, nous donnons l’asymptotique générale des nombres d...
متن کاملPartition Statistics and q - Bell Numbers ( q = − 1 )
We study three types of q-Bell numbers that arise as generating functions for some well known statistics on the family of partitions of a finite set, evaluating these numbers when q = −1. Among the numbers that arise in this way are (1) Fibonacci numbers and (2) numbers occurring in the study of fermionic oscillators.
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1997
ISSN: 0168-0072
DOI: 10.1016/s0168-0072(97)00038-9