A Note on the $\gamma$-Coefficients of the Tree Eulerian Polynomial

[摘要] We consider the generating polynomial of the number of rooted trees on the set $\{1,2,\dots,n\}$ counted by the number of descending edges (a parent with a greater label than a child). This polynomial is an extension of the descent generating polynomial o

[学科分类] 离散数学和组合数学

[关键词] Gamma positivity;Eulerian polynomial;Rooted trees