Geodesic
On the Lattice Property of Shard Orders
Séminaire lotharingien de combinatoire, 80B (2018) 
Henri Mühle. On the Lattice Property of Shard Orders. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a3/
@article{SLC_2018_80B_a3,
     author = {Henri M\"uhle},
     title = {On the {Lattice} {Property} of {Shard} {Orders}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2018},
     volume = {80B},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a3/}
}
TY  - JOUR
AU  - Henri Mühle
TI  - On the Lattice Property of Shard Orders
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a3/
ID  - SLC_2018_80B_a3
ER  - 
%0 Journal Article
%A Henri Mühle
%T On the Lattice Property of Shard Orders
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a3/
%F SLC_2018_80B_a3

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

Let L be a congruence-uniform lattice. In this article, we investigate the shard order on L that was introduced by N.~Reading. When L can be realized as a poset of regions of a hyperplane arrangement the shard order is always a lattice. For general L, however, this fails. We provide a necessary condition for the shard order to be a lattice, and we show how to construct a congruence-uniform lattice L' from L such that the shard order on L' fails to be a lattice.