Counting permutations by runs

DOI10.1016/J.JCTA.2016.04.002zbMath1336.05010arXiv1505.02308OpenAlexW2237129737MaRDI QIDQ285069

Yan Zhuang

Publication date: 18 May 2016

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

Full work available at URL: https://arxiv.org/abs/1505.02308

zbMATH Keywords

permutationsnoncommutative symmetric functionsincreasing runspeaksvalleys

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Permutations, words, matrices (05A05) Symmetric functions and generalizations (05E05)

Related Items (18)

Eulerian polynomials and descent statistics ⋮ Shuffle-compatible permutation statistics ⋮ The Dumont ansatz for the Eulerian polynomials, peak polynomials and derivative polynomials ⋮ A grammatical calculus for peaks and runs of permutations ⋮ Stirling permutation codes ⋮ Positivity of Narayana polynomials and Eulerian polynomials ⋮ Triangular recurrences, generalized Eulerian numbers, and related number triangles ⋮ Plethystic formulas for permutation enumeration ⋮ Unnamed Item ⋮ Subalgebras of Solomon's descent algebra based on alternating runs ⋮ An asymptotic distribution theory for Eulerian recurrences with applications ⋮ Jacobian elliptic functions and a family of bivariate peak polynomials ⋮ David-Barton type identities and alternating run polynomials ⋮ Homomorphisms on noncommutative symmetric functions and permutation enumeration ⋮ \(\gamma\)-positivity and partial \(\gamma\)-positivity of descent-type polynomials ⋮ Hopping from Chebyshev polynomials to permutation statistics ⋮ A lifting of the Goulden-Jackson cluster method to the Malvenuto-Reutenauer algebra ⋮ Reciprocals of exponential polynomials and permutation enumeration

Uses Software

• OEIS

Cites Work

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• Counting permutations by alternating descents
• Longest alternating subsequences of permutations
• Introduction to partially ordered patterns
• Variations on descents and inversions in permutations
• Noncommutative symmetric functions
• A combinatorial proof of a result of Gessel and Greene
• Enumeration of permutations of \((1, \ldots, n)\) by number of maxima
• Combinatorics of Permutations
• A Coloring Problem
• Decomposition Based Generating Functions for Sequences

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