The γ-positivity of basic Eulerian polynomials via group actions

2014/11/12 by Zhicong Lin, Jiang Zeng, Lin, Zhicong +1
Agricultural and Biological Sciences · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Botanical Research and Chemistry #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1411.3397

openalex publication_date 2014/11/12 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We provide combinatorial interpretation for the γ-coefficients of the basic Eulerian polynomials that enumerate permutations by the excedance statistic and the major index as well as the corresponding γ-coefficients for derangements. Our results refine the classical γ-positivity results for the Eulerian polynomials and the derangement polynomials. The main tools are Brändén's modified Foata--Strehl action on permutations and the recent triple statistic (des, rix,aid) equidistibuted with (exc, fix, maj).

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