"Non UBC"@en .
"DSpace"@en .
"Ellingham, Mark"@en .
"2019-03-20T02:01:39Z"@en .
"2018-09-20T15:15"@en .
"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."@en .
"https://circle.library.ubc.ca/rest/handle/2429/68957?expand=metadata"@en .
"41.0"@en .
"video/mp4"@en .
""@en .
"Author affiliation: Vanderbilt University"@en .
"Oaxaca (Mexico : State)"@en .
"10.14288/1.0377187"@en .
"eng"@en .
"Unreviewed"@en .
"Vancouver : University of British Columbia Library"@en .
"Banff International Research Station for Mathematical Innovation and Discovery"@en .
"Attribution-NonCommercial-NoDerivatives 4.0 International"@en .
"http://creativecommons.org/licenses/by-nc-nd/4.0/"@en .
"Faculty"@en .
"BIRS Workshop Lecture Videos (Oaxaca (Mexico : State))"@en .
"Mathematics"@en .
"Combinatorics"@en .
"Group theory and generalizations"@en .
"Discrete mathematics"@en .
"Distinguishing partitions and asymmetric uniform hypergraphs"@en .
"Moving Image"@en .
"http://hdl.handle.net/2429/68957"@en .