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A Note On The Γ-Coefficients Of The Tree Eulerian Polynomial, Rafael S. González D'León
A Note On The Γ-Coefficients Of The Tree Eulerian Polynomial, Rafael S. González D'León
Mathematics Faculty Publications
We consider the generating polynomial of the number of rooted trees on the set {1,2,...,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 of the set of permutations of a totally ordered n-set, known as the Eulerian polynomial. We show how this extension shares some of the properties of the classical one. A classical product formula shows that this polynomial factors completely over the integers. From this product formula it can be concluded that this polynomial has positive coefficients …