منابع مشابه
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].
متن کاملSTATISTICS ON ORDERED PARTITIONS OF SETS AND q-STIRLING NUMBERS
An ordered partition of [n] := {1, 2, . . . , n} is a sequence of its disjoint subsets whose union is [n]. The number of ordered partitions of [n] with k blocks is k!S(n, k), where S(n, k) is the Stirling number of second kind. In this paper we prove some refinements of this formula by showing that the generating function of some statistics on the set of ordered partitions of [n] with k blocks ...
متن کاملNegative q-Stirling numbers
The notion of the negative q-binomial was recently introduced by Fu, Reiner, Stanton and Thiem. Mirroring the negative q-binomial, we show the classical q-Stirling numbers of the second kind can be expressed as a pair of statistics on a subset of restricted growth words. The resulting expressions are polynomials in q and 1 + q. We extend this enumerative result via a decomposition of the Stirli...
متن کاملRook Theory, Generalized Stirling Numbers and (p, q)-Analogues
In this paper, we define two natural (p, q)-analogues of the generalized Stirling numbers of the first and second kind S(α, β, r) and S(α, β, r) as introduced by Hsu and Shiue [17]. We show that in the case where β = 0 and α and r are nonnegative integers both of our (p, q)-analogues have natural interpretations in terms of rook theory and derive a number of generating functions for them. We al...
متن کاملBaxter Algebras, Stirling Numbers and Partitions
Recent developments of Baxter algebras have lead to applications to combinatorics, number theory and mathematical physics. We relate Baxter algebras to Stirling numbers of the first kind and the second kind, partitions and multinomial coefficients. This allows us to apply congruences from number theory to obtain congruences in Baxter algebras.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1994
ISSN: 0097-3165
DOI: 10.1016/0097-3165(94)90090-6