A combinatorial proof of the log-concavity of the numbers of permutations with \(k\) runs
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Publication:1570759
DOI10.1006/jcta.1999.3040zbMath0951.05002arXivmath/9902020OpenAlexW2126537558MaRDI QIDQ1570759
Richard Ehrenborg, Miklós Bóna
Publication date: 13 December 2000
Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/9902020
Related Items (19)
Generating functions of permutations with respect to their alternating runs ⋮ Enumeration of permutations by number of alternating runs ⋮ Lattice paths and \((n - 2)\)-stack sortable permutations ⋮ Context-free grammars, generating functions and combinatorial arrays ⋮ An explicit formula for the number of permutations with a given number of alternating runs ⋮ Counting signed permutations by their alternating runs ⋮ Unnamed Item ⋮ Counting permutations by their alternating runs ⋮ Logarithmic behavior of some combinatorial sequences ⋮ Seven (lattice) paths to log-convexity ⋮ Preservation of log-concavity on summation ⋮ Subalgebras of Solomon's descent algebra based on alternating runs ⋮ Log-concavity of the excedance enumerators in positive elements of type A and type B Coxeter groups ⋮ Run Distribution Over Flattened Partitions ⋮ Interlacing log-concavity of the derangement polynomials and the Eulerian polynomials ⋮ The descent statistic on involutions is not log-concave ⋮ David-Barton type identities and alternating run polynomials ⋮ Tree descent polynomials: unimodality and central limit theorem ⋮ Enumerating \(S_n\) by associated transpositions and linear extensions of finite posets
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