Geodesic
Playing Jeu De Taquin on d-Complete Posets
Séminaire lotharingien de combinatoire, Tome 74 (2015-2018)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

Using a modified version of jeu de taquin, Novelli, Pak and Stoyanovskii gave a bijective proof of the hook-length formula for counting standard Young tableaux of fixed shape. In this paper we consider a natural extension of jeu de taquin to arbitrary posets. Given a poset P, jeu de taquin defines a map from the set of bijective labelings of the poset elements with {1,2,...,|P|} to the set of linear extensions of the poset. One question of particular interest is for which posets this map yields each linear extension equally often. We analyze the double-tailed diamond poset Dm,n and show that uniform distribution is obtained if and only if Dm,n is d-complete. Furthermore, we observe that the extended hook-length formula for counting linear extensions on d-complete posets provides a combinatorial answer to a seemingly unrelated question, namely: Given a uniformly random standard Young tableau of fixed shape, what is the expected value of the left-most entry in the second row? 

@article{SLC_2015-2018_74_a3,
     author = {Lukas Riegler and Christoph Neumann},
     title = {Playing {Jeu} {De} {Taquin} on {d-Complete} {Posets}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {74},
     year = {2015-2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2015-2018_74_a3/}
}
TY  - JOUR
AU  - Lukas Riegler
AU  - Christoph Neumann
TI  - Playing Jeu De Taquin on d-Complete Posets
JO  - Séminaire lotharingien de combinatoire
PY  - 2015-2018
VL  - 74
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2015-2018_74_a3/
ID  - SLC_2015-2018_74_a3
ER  - 
%0 Journal Article
%A Lukas Riegler
%A Christoph Neumann
%T Playing Jeu De Taquin on d-Complete Posets
%J Séminaire lotharingien de combinatoire
%D 2015-2018
%V 74
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2015-2018_74_a3/
%F SLC_2015-2018_74_a3
Lukas Riegler; Christoph Neumann. Playing Jeu De Taquin on d-Complete Posets. Séminaire lotharingien de combinatoire, Tome 74 (2015-2018). http://geodesic.mathdoc.fr/item/SLC_2015-2018_74_a3/