Non UBC
DSpace
Ellingham, Mark
2019-03-20T02:01:39Z
2018-09-20T15:15
In 2011 Ellingham and Schroeder introduced the idea of a "distinguishing partition" for an action of a group $\Gamma$ on a set $X$, namely a partition of $X$ that is preserved by no nontrivial element of $\Gamma$. As a special case, a distinguishing partition of a graph is a partition of the vertex set that is preserved by no nontrivial automorphism. Distinguishing partitions are weaker at breaking symmetry than distinguishing colourings, and not every graph has a distinguishing partition. We discuss our work with Schroeder which linked distinguishing partitions of complete equipartite graphs with asymmetric uniform hypergraphs. We find a function $f(n)$ such that a distinguishing partition for $K_{m(n)}=K_{n,n,\ldots,n}$, or equivalently for the wreath product action $S_n \wr S_m$, exists if and only if $m\geq f(n)$. We also discuss some other work on distinguishing partitions of complete multipartite graphs by Michael Goff.
https://circle.library.ubc.ca/rest/handle/2429/68957?expand=metadata
41.0
video/mp4
Author affiliation: Vanderbilt University
Oaxaca (Mexico : State)
10.14288/1.0377187
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Faculty
BIRS Workshop Lecture Videos (Oaxaca (Mexico : State))
Mathematics
Combinatorics
Group theory and generalizations
Discrete mathematics
Distinguishing partitions and asymmetric uniform hypergraphs
Moving Image
http://hdl.handle.net/2429/68957