In this paper, we study tree–like tableaux, combinatorial objects which exhibit a natural tree structure and are connected to the partially asymmetric simple exclusion process (PASEP). There was a conjecture made on the total number of corners in tree–like tableaux and the total number of corners in symmetric tree–like tableaux. In this paper, we prove both conjectures. Our proofs are based off of the bijection with permutation tableaux or type–B permutation tableaux and consequently, we also prove results for these tableaux. In addition, we derive the limiting distribution of the number of occupied corners in random tree–like tableaux and random symmetric tree–like tableaux.
@article{10_37236_5712,
author = {Pawe{\l} Hitczenko and Amanda Lohss},
title = {Corners in tree-like tableaux},
journal = {The electronic journal of combinatorics},
year = {2016},
volume = {23},
number = {4},
doi = {10.37236/5712},
zbl = {1351.05229},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5712/}
}
TY - JOUR
AU - Paweł Hitczenko
AU - Amanda Lohss
TI - Corners in tree-like tableaux
JO - The electronic journal of combinatorics
PY - 2016
VL - 23
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/5712/
DO - 10.37236/5712
ID - 10_37236_5712
ER -
%0 Journal Article
%A Paweł Hitczenko
%A Amanda Lohss
%T Corners in tree-like tableaux
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/5712/
%R 10.37236/5712
%F 10_37236_5712
Paweł Hitczenko; Amanda Lohss. Corners in tree-like tableaux. The electronic journal of combinatorics, Tome 23 (2016) no. 4. doi: 10.37236/5712
