Séminaire Lotharingien de Combinatoire, 84B.17 (2020), 12 pp.

Matjaž Konvalinka and Vasu Tewari

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.

Received: November 20, 2019. Accepted: February 20, 2020. Final version: April 30, 2020.

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