Geodesic
EW-tableaux, Le-tableaux, tree-like tableaux and the abelian sandpile model
Thomas Selig1 ; Jason P. Smith1 ; Einar Steingrímsson1
1University of Strathclyde
The electronic journal of combinatorics, Tome 25 (2018) no. 3
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

A EW-tableau is a certain 0/1-filling of a Ferrers diagram, corresponding uniquely to an acyclic orientation, with a unique sink, of a certain bipartite graph called a Ferrers graph. We give a bijective proof of a result of Ehrenborg and van Willigenburg showing that EW-tableaux of a given shape are equinumerous with permutations with a given set of excedances. This leads to an explicit bijection between EW-tableaux and the much studied Le-tableaux, as well as the tree-like tableaux introduced by Aval, Boussicault and Nadeau.We show that the set of EW-tableaux on a given Ferrers diagram are in 1-1 correspondence with the minimal recurrent configurations of the Abelian sandpile model on the corresponding Ferrers graph.Another bijection between EW-tableaux and tree-like tableaux, via spanning trees on the corresponding Ferrers graphs, connects the tree-like tableaux to the minimal recurrent configurations of the Abelian sandpile model on these graphs. We introduce a variation on the EW-tableaux, which we call NEW-tableaux, and present bijections from these to Le-tableaux and tree-like tableaux. We also present results on various properties of and statistics on EW-tableaux and NEW-tableaux, as well as some open problems on these.
DOI : 10.37236/7480
Classification : 05A19, 05A05, 05A15, 60J10
Mots-clés : permutation tableaux, EW-tableaux, Le-tableaux, tree-like tableaux, NEW-tableaux, abelian sandpile model, permutation statistics

Thomas Selig  1   ; Jason P. Smith  1   ; Einar Steingrímsson  1

1 University of Strathclyde 
@article{10_37236_7480,
     author = {Thomas Selig and Jason P. Smith and Einar Steingr{\'\i}msson},
     title = {EW-tableaux, {Le-tableaux,} tree-like tableaux and the abelian sandpile model},
     journal = {The electronic journal of combinatorics},
     year = {2018},
     volume = {25},
     number = {3},
     doi = {10.37236/7480},
     zbl = {1393.05054},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/7480/}
}
TY  - JOUR
AU  - Thomas Selig
AU  - Jason P. Smith
AU  - Einar Steingrímsson
TI  - EW-tableaux, Le-tableaux, tree-like tableaux and the abelian sandpile model
JO  - The electronic journal of combinatorics
PY  - 2018
VL  - 25
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.37236/7480/
DO  - 10.37236/7480
ID  - 10_37236_7480
ER  - 
%0 Journal Article
%A Thomas Selig
%A Jason P. Smith
%A Einar Steingrímsson
%T EW-tableaux, Le-tableaux, tree-like tableaux and the abelian sandpile model
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/7480/
%R 10.37236/7480
%F 10_37236_7480
Thomas Selig; Jason P. Smith; Einar Steingrímsson. EW-tableaux, Le-tableaux, tree-like tableaux and the abelian sandpile model. The electronic journal of combinatorics, Tome 25 (2018) no. 3. doi: 10.37236/7480

Cité par Sources :