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Leroux, Pierre

Reduced matrices and q-log-concavity properties of q-Stirling numbers. (English) Zbl 0704.05003

J. Comb. Theory, Ser. A 54, No. 1, 64-84 (1990).
Author’s abstract: “We prove the q-log-concavity of the q-Stirling number of the second kind, which was recently conjectured by Lynne Butler, by suitably extending her injective proof of the analogous property of the q-binomial coefficients. For this we introduce new combinatorial interpretations of Stirling numbers of both kinds in terms of “0-1 tableaux” inspired from a row-reduced echelon matrix representation of restricted growth functions. Other related results, methods, counterexamples, and conjectures are discussed.”
Reviewer: J.Cigler

Cited in 40 Documents

MSC:

05A15 Exact enumeration problems, generating functions
05A40 Umbral calculus
11B73 Bell and Stirling numbers
05E10 Combinatorial aspects of representation theory

Keywords:

q-log-concavity; q-Stirling number of the second kind; 0-1 tableaux
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\textit{P. Leroux}, J. Comb. Theory, Ser. A 54, No. 1, 64--84 (1990; Zbl 0704.05003)
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References:

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