The $\gamma$-coefficients of Eulerian polynomials were first considered by Foata and Schützenberger. In this paper, we provide combinatorial interpretations for the $\gamma$-coefficients arising from the segmented permutations and segmented derangements via Brändén’s modified Foata–Strehl action. We also give the combinatorial interpretations of $\gamma$-coefficients for the $(>,\le ,-)$-avoiding inversion sequences via continued fractions.

中文翻译：

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这 $\gamma$分段排列中出现的正系数

这 $\gamma$Foata和Schützenberger首先考虑了欧拉多项式的-系数。在本文中，我们为$\gamma$-coefficients从产生分段排列和分段紊乱通过布兰登的修改Foata-斯切尔行动。我们还给出了的组合解释$\gamma$-的系数 $（>，\le ，-）$-通过连续分数避免反演序列。