Subgroups of the symmetric group $S_n$ act on $C^n$ (the $n$-fold product $C \times \cdots \times C$ of a chain $C$) by permuting coordinates, and induce automorphisms of the power $C^n$. For certain families of subgroups of $S_n$, the quotients defined by these groups can be shown to have symmetric chain decompositions (SCDs). These SCDs allow us to enlarge the collection of subgroups $G$ of $S_n$ for which the quotient $\mathbf{2}^n/G$ on the Boolean lattice $\mathbf{2}^n$ is a symmetric chain order (SCO). The methods are also used to provide an elementary proof that quotients of powers of SCOs by cyclic groups are SCOs.
@article{10_37236_5073,
author = {Dwight Duffus and Kyle Thayer},
title = {Symmetric chain decompositions of quotients by wreath products.},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {2},
doi = {10.37236/5073},
zbl = {1315.06003},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5073/}
}
TY - JOUR
AU - Dwight Duffus
AU - Kyle Thayer
TI - Symmetric chain decompositions of quotients by wreath products.
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/5073/
DO - 10.37236/5073
ID - 10_37236_5073
ER -
%0 Journal Article
%A Dwight Duffus
%A Kyle Thayer
%T Symmetric chain decompositions of quotients by wreath products.
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/5073/
%R 10.37236/5073
%F 10_37236_5073
Dwight Duffus; Kyle Thayer. Symmetric chain decompositions of quotients by wreath products.. The electronic journal of combinatorics, Tome 22 (2015) no. 2. doi: 10.37236/5073
