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.
@article{10_37236_8484,
author = {Matja\v{z} Konvalinka and Vasu Tewari},
title = {Smirnov trees},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {3},
doi = {10.37236/8484},
zbl = {1417.05030},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8484/}
}
TY - JOUR
AU - Matjaž Konvalinka
AU - Vasu Tewari
TI - Smirnov trees
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/8484/
DO - 10.37236/8484
ID - 10_37236_8484
ER -
%0 Journal Article
%A Matjaž Konvalinka
%A Vasu Tewari
%T Smirnov trees
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/8484/
%R 10.37236/8484
%F 10_37236_8484
Matjaž Konvalinka; Vasu Tewari. Smirnov trees. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/8484
