p, q-Stirling numbers and set partition statistics

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...

Partition Lattice q-Analogs Related to q-Stirling Numbers

Abstract We construct a family of partially ordered sets (posets) that are q-analogs of the set partition lattice. They are different from the q-analogs proposed by Dowling [5]. One of the important features of these posets is that their Whitney numbers of the first and second kind are just the q-Stirling numbers of the first and second kind, respectively. One member of this family [4] can be c...

P-Partitioins and q-Stirling Numbers

New q-analogs of Stirling numbers of the second kind(and the first kined) are derived from a poset on [2k] using Stanley’s P -partition theory [?]. We also generalize to the poset on the set [rk].

Partition Statistics and Fermionic Stirling and Bell Numbers

Partition 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.