Alternating permutations and symmetric functions

DOI10.1016/j.jcta.2006.06.008zbMath1118.05002arXivmath/0603520OpenAlexW1974226462MaRDI QIDQ878952

Richard P. Stanley

Publication date: 4 May 2007

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

Full work available at URL: https://arxiv.org/abs/math/0603520

zbMATH Keywords

symmetric functionEuler numberalternating permutationumbral

Mathematics Subject Classification ID

Umbral calculus (05A40) Exact enumeration problems, generating functions (05A15) Permutations, words, matrices (05A05) Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Asymptotic enumeration (05A16)

Related Items

The number of cycles with a given descent set, The plethystic inverse of the odd Lie representations, Up-down coefficients for permutations, Unimodal permutations and almost-increasing cycles, Pattern avoiding alternating involutions, On refinements of Wilf-equivalence for involutions, Exact and asymptotic enumeration of cyclic permutations according to descent set, Equidistribution of set-valued statistics on standard Young tableaux and transversals, Pattern avoidance for alternating permutations and Young tableaux, Symmetric generating functions and Euler-Stirling statistics on permutations, Plethystic formulas for permutation enumeration, Fix-Mahonian calculus. I: Two transformations, Foulkes characters, Eulerian idempotents, and an amazing matrix, Combinatorics of generalized \(q\)-Euler numbers, Koszul duality for monoids and the operad of enriched rooted trees, Permutations with extremal number of fixed points, Labeled binary trees, subarrangements of the Catalan arrangements, and Schur positivity

Uses Software

• EHRENBORG

Cites Work

• Symmetric functions and P-recursiveness
• Ramanujan's ``lost notebook. I: Partial Theta-functions
• Enumeration of permutations with prescribed up-down and inversion sequences
• Tangent and secant numbers and representations of symmetric groups
• Advanced determinant calculus
• Counting permutations with given cycle structure and descent set
• Doubly alternating Baxter permutations are Catalan
• Enumeration of up-down sequences
• Weighted Derangements and the Linearization Coefficients of Orthogonal Sheffer Polynomials
• The Classical Umbral Calculus
• Classical Orthogonal Polynomials as Moments
• Multiplicities of Higher Lie Characters
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