Smirnov Trees

Abstract

We introduce a generalization of Smirnov words in the context of labeled binary trees, which we call Smirnov trees. We study the generating function for ascent-descent statistics on Smirnov trees and establish that it is $e$-positive, which is akin to the classical case of Smirnov words. Our proof relies on an intricate weight-preserving bijection.

arXiv comment23 pages