An explicit formula for the number of permutations with a given number of alternating runs

DOI10.1016/j.jcta.2012.05.005zbMath1246.05011arXiv1110.6779OpenAlexW2091870483MaRDI QIDQ444901

Shi-Mei Ma

Publication date: 24 August 2012

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.6779

zbMATH Keywords

permutationsEulerian polynomialsalternating runsderivative polynomials

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Permutations, words, matrices (05A05) Symmetric groups (20B30)

Related Items (15)

The peak statistics on simsun permutations ⋮ ON -VECTORS AND THE DERIVATIVES OF THE TANGENT AND SECANT FUNCTIONS ⋮ Enumeration of permutations by number of alternating runs ⋮ Context-free grammars, generating functions and combinatorial arrays ⋮ Counting permutations by simsun successions ⋮ Enumeration of permutations by number of alternating descents ⋮ Counting signed permutations by their alternating runs ⋮ Unnamed Item ⋮ Several variants of the Dumont differential system and permutation statistics ⋮ Subalgebras of Solomon's descent algebra based on alternating runs ⋮ Enumeration of type \(D\) permutations with alternating runs ⋮ An asymptotic distribution theory for Eulerian recurrences with applications ⋮ Run Distribution Over Flattened Partitions ⋮ David-Barton type identities and alternating run polynomials ⋮ The \(1 / k\)-Eulerian polynomials and \(k\)-Stirling permutations

Uses Software

• OEIS

Cites Work

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• Derivative polynomials and enumeration of permutations by number of interior and left peaks
• Longest alternating subsequences of permutations
• Derivative polynomials and closed-form higher derivative formulae
• A combinatorial proof of the log-concavity of the numbers of permutations with \(k\) runs
• Functions with derivatives given by polynomials in the function itself or a related function
• Counting permutations by their alternating runs
• Tangent numbers and operators
• Combinatorial extreme value distributions
• Derivative Polynomials for Tangent and Secant

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