Denert's Permutation Statistic Is Indeed Euler‐Mahonian

1990/07/01 by Dominique Foata, Doron Zeilberger · 13 citations
Mathematics · Computer Science · #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models #Advanced Mathematical Identities

paper · doi:10.1002/sapm199083131

Abstract

A conjecture by Marleen Denert concerning a bivariate statistic on the permutation group is proved. The statistic has the same distribution as the pair consisting of the number of descents and the major index.

Cited by

• Cyclic sieving phenomena via combinatorics of continued fractions
• Cyclic sieving on permutations -- an analysis of maps and statistics in the FindStat database
• Crossings and alignments of permutations
• Some multivariate master polynomials for permutations, set partitions, and perfect matchings, and their continued fractions
• Classical continued fractions for some multivariate polynomials generalizing the Genocchi and median Genocchi numbers
• Fractions Continues,q-Nombres de Catalan etq-Polynômes de Genocchi
• Statistics on Wreath Products
• Han's Bijection via Permutation Codes
• The pinnacle set of a permutation
• An involution for trivariate symmetries of vincular patterns
• q-Rook polynomials and matrices over finite fields
• Moments des Polynômes Orthogonaux Unitaires de Sheffer Généralisés et Spécialisations
• New r-Euler--Mahonian statistics involving Denert's statistic

Related

• New r-Euler--Mahonian statistics involving Denert's statistic
• On a conjecture concerning the r-Euler-Mahonian statistic on permutations
• Further results on r-Euler-Mahonian statistics
• A new bijective proof of Babson and Steingr'ımsson's conjecture
• On Denert's statistic