Major Index and Inversion Number of Permutations

DOI10.1002/mana.19780830111zbMath0319.05002OpenAlexW2145596344MaRDI QIDQ4081257

Schützenberger, Marcel-Paul, Foata, Dominique

Publication date: 1978

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.19780830111

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Permutations, words, matrices (05A05) Representations of finite symmetric groups (20C30) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Permutation groups (20B99)

Related Items (72)

Eulerian polynomials and descent statistics ⋮ On the relationship between combinatorial functions and representation theory ⋮ NONCOMMUTATIVE SYMMETRIC FUNCTIONS VI: FREE QUASI-SYMMETRIC FUNCTIONS AND RELATED ALGEBRAS ⋮ A combinatorial approach to the \(q,t\)-symmetry relation in Macdonald polynomials ⋮ Diagonal invariants and the refined multimahonian distribution. ⋮ Counting permutations by congruence class of major index ⋮ Toward the Schur expansion of Macdonald polynomials ⋮ Unnamed Item ⋮ Permutation statistics and \((k,\ell)\)-hook Schur functions ⋮ On some Euler-Mahonian distributions ⋮ Block decomposition of permutations and Schur-positivity ⋮ Cycle type and descent set in wreath products ⋮ Eulerian quasisymmetric functions ⋮ The doubloon polynomial triangle ⋮ 0-Hecke algebra actions on coinvariants and flags ⋮ On permutation weights and \(q\)-Eulerian polynomials ⋮ Branching formula for \(q\)-Littlewood--Richardson coefficients ⋮ A complete enumeration of Ballot permutations avoiding sets of small patterns ⋮ Euler-Mahonian triple set-valued statistics on permutations ⋮ Homomesies on permutations: An analysis of maps and statistics in the FindStat database ⋮ A natural idempotent in the descent algebra of a finite Coxeter group ⋮ Generalized Worpitzky identities with applications to permutation enumeration ⋮ Signed mahonians on some trees and parabolic quotients ⋮ q-hook length formulas for forests ⋮ Fonctions symétriques et séries hypergéométriques basiques multivariées ⋮ An analogue of Kummer congruences for \(q\)-Euler numbers ⋮ Signed words and permutations. IV: Fixed and pixed points ⋮ Statistiques d'ordre sur les permutations colorées. (Order statistics on coloured permutations) ⋮ Permutation statistics and linear extensions of posets ⋮ Matrices, characters and descents ⋮ Fix-Mahonian calculus. III: a quadruple distribution ⋮ The \(\gamma\)-positivity of basic Eulerian polynomials via group actions ⋮ Trees, functional equations, and combinatorial Hopf algebras ⋮ A \(q\)-analogue of generalized Eulerian polynomials with applications ⋮ Fix-Mahonian calculus. II: Further statistics ⋮ A simple transformation for Mahonian statistics on labelings of rake posets ⋮ The signed Eulerian numbers ⋮ An involution for signed Eulerian numbers ⋮ New Euler-Mahonian statistics on permutations and words ⋮ Enumeration by associated reflections on Coxeter systems ⋮ Equidistribution of negative statistics and quotients of Coxeter groups of type \(B\) and \(D\) ⋮ Multibasic Eulerian Polynomials ⋮ \(q\)-partition algebra combinatorics ⋮ Some remarks on sign-balanced and maj-balanced posets ⋮ (\(q,t\))-analogues and \(GL_{n}({\mathbb{F}}_{q})\) ⋮ Signed Mahonians ⋮ Note on the minimal permutations ⋮ Structure of the Malvenuto-Reutenauer Hopf algebra of permutations ⋮ Parabolically induced functions and equidistributed pairs ⋮ Generalized statistics on \(S_{n}\) and pattern avoidance ⋮ Permutation statistics and the \(q,t\)-Catalan sequence ⋮ Fonctions symétriques associées à des suites classiques de nombres ⋮ Permutation statistics on the alternating group ⋮ Statistics on wreath products, perfect matchings, and signed words ⋮ The flag major index and group actions on polynomial rings. ⋮ Specializations of colored quasisymmetric functions and Euler-Mahonian identities ⋮ Equi-distribution over descent classes of the hyperoctahedral group ⋮ Signed Mahonian polynomials for major and sorting indices ⋮ Signed Mahonian identities on permutations with subsequence restrictions ⋮ Signed Mahonian identities on permutations with subsequence restrictions ⋮ A combinatorial model for the Macdonald polynomials ⋮ Unnamed Item ⋮ \(q\)-hook length formulas for signed labeled forests ⋮ Popularity of patterns over \(d\)-equivalence classes of words and permutations ⋮ Some statistics for Fibonacci tableaux ⋮ Enumerating \(S_n\) by associated transpositions and linear extensions of finite posets ⋮ The maximal-inversion statistic and pattern-avoiding permutations ⋮ Signed words and permutations, I: A fundamental transformation ⋮ Mahonian STAT on rearrangement class of words ⋮ 𝑞-Eulerian polynomials: Excedance number and major index ⋮ Descent classes of permutations with a given number of fixed points ⋮ Character formulas and descents for the hyperoctahedral group

Cites Work

This page was built for publication: Major Index and Inversion Number of Permutations