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

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


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


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