On γ-positive polynomials arising in Pattern Avoidance

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• 作者：Zhicong Lin^a ; ^b ; ^{lin@nims.re.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：05A05 ; 05A15 ; 05A20
• 刊名：Advances in Applied Mathematics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：82
• 期：Complete
• 页码：1-22
• 全文大小：448 K

文摘

A classical result of Foata and Schützenberger states that the γ-coefficients of the Eulerian polynomials enumerate permutations without double descents by the number of descents. In this paper, based on works of Cheng et al. and Stankova, we provide similar combinatorial interpretations for the γ  -coefficients of the inversion polynomials on 321-avoiding permutations and the descent polynomials on Separable permutations (or (2413,3142)$(2413,3142)$-avoiding permutations) and (1342,2431)$(1342,2431)$-avoiding permutations. Some further open problems are also proposed.