منابع مشابه
q-Stirling Identities Revisited
We give combinatorial proofs of q-Stirling identities using restricted growth words. This includes a poset theoretic proof of Carlitz’s identity, a new proof of the q-Frobenius identity of Garsia and Remmel and of Ehrenborg’s Hankel q-Stirling determinantal identity. We also develop a two parameter generalization to unify identities of Mercier and include a symmetric function version.
متن کاملMultiple Stirling Number Identities
A remarkable multiple analogue of the Stirling numbers of the first and second kind was recently constructed by the author. Certain summation identities, and related properties of this family of multiple special numbers are investigated in the present paper.
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 کاملArithmetic Identities Involving Genocchi and Stirling Numbers
Guodong Liu Department of Mathematics, Huizhou University, Huizhou, Guangdong 516015, China Correspondence should be addressed to Guodong Liu, [email protected] Received 18 June 2009; Accepted 12 August 2009 Recommended by Leonid Berezansky An explicit formula, the generalized Genocchi numbers, was established and some identities and congruences involving the Genocchi numbers, the Bernoul...
متن کاملAutomated Proofs for Some Stirling Number Identities
We present computer-generated proofs of some summation identities for (q-)Stirling and (q-)Eulerian numbers that were obtained by combining a recent summation algorithm for Stirling number identities with a recurrence solver for difference fields.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2018
ISSN: 1077-8926
DOI: 10.37236/6829