Geodesic
Rowmotion and generalized toggle groups
Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 1.

Voir la notice de l'article provenant de la source Episciences

We generalize the notion of the toggle group, as defined in [P. Cameron-D. Fon-der-Flaass '95] and further explored in [J. Striker-N. Williams '12], from the set of order ideals of a poset to any family of subsets of a finite set. We prove structure theorems for certain finite generalized toggle groups, similar to the theorem of Cameron and Fon-der-Flaass in the case of order ideals. We apply these theorems and find other results on generalized toggle groups in the following settings: chains, antichains, and interval-closed sets of a poset; independent sets, vertex covers, acyclic subgraphs, and spanning subgraphs of a graph; matroids and convex geometries. We generalize rowmotion, an action studied on order ideals in [P. Cameron-D. Fon-der-Flaass '95] and [J. Striker-N. Williams '12], to a map we call cover-closure on closed sets of a closure operator. We show that cover-closure is bijective if and only if the set of closed sets is isomorphic to the set of order ideals of a poset, which implies rowmotion is the only bijective cover-closure map. 
@article{DMTCS_2018_20_1_a14,
     author = {Striker, Jessica},
     title = {Rowmotion and generalized toggle groups},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2018},
     doi = {10.23638/DMTCS-20-1-17},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-20-1-17/}
}
TY  - JOUR
AU  - Striker, Jessica
TI  - Rowmotion and generalized toggle groups
JO  - Discrete mathematics & theoretical computer science
PY  - 2018
VL  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-20-1-17/
DO  - 10.23638/DMTCS-20-1-17
LA  - en
ID  - DMTCS_2018_20_1_a14
ER  - 
%0 Journal Article
%A Striker, Jessica
%T Rowmotion and generalized toggle groups
%J Discrete mathematics & theoretical computer science
%D 2018
%V 20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-20-1-17/
%R 10.23638/DMTCS-20-1-17
%G en
%F DMTCS_2018_20_1_a14
Striker, Jessica. Rowmotion and generalized toggle groups. Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 1. doi : 10.23638/DMTCS-20-1-17. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-20-1-17/

Cité par Sources :