@prefix vivo: . @prefix edm: . @prefix dcterms: . @prefix dc: . @prefix skos: . @prefix ns0: . vivo:departmentOrSchool "Non UBC"@en ; edm:dataProvider "DSpace"@en ; dcterms:creator "Tucker, Thomas"@en ; dcterms:issued "2019-03-17T08:34:37Z"@en, "2018-09-17T09:31"@en ; dcterms:description """Given a group $A$ acting on a set $X$, the distinguishing number, or asymmetric coloring number, denoted $D(A,X)$ or $ACN(A,X)$, is the smallest $k$ such that $X$ has a $k$-coloring where the only elements of $A$ preserving the coloring fix all elements of $X$, thus "breaking" the symmetry of $X$ under $A$. Albertson and Collins [1996] introduced and named $D(G)$ in the context of a graph $G$ with $A=Aut(G), X=V(G)$, but precedents include Babai's work [1977] on regular trees, Cameron et al.\\ [1984] and Seress [1997] on regular orbits for a primitive permutation group acting on the set of subsets of $X$, and work of many authors on the graph isomorphism problem using colors to "individualize" vertices. This talk will survey various aspects of symmetry breaking: contexts other than graphs (such as maps), bounds relating $D(G)$ and the maximal degree of $G$, variations of $D(G)$ where the coloring is proper or where edges are colored instead of vertices. An underlying theme is the role of the elementary "Motion Lemma'' (Cameron et al. [1984] and Russel and Sundaram [1997]) that $D\\leq 2$ when $m(A)>2\\log_2(|A|)$, where $m(A)$ is the minimum number of elements of $X$ moved by any element of $A$ not acting as the identity on $X$."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/68822?expand=metadata"@en ; dcterms:extent "46.0"@en ; dc:format "video/mp4"@en ; skos:note ""@en, "Author affiliation: Colgate University"@en ; edm:isShownAt "10.14288/1.0377009"@en ; dcterms:language "eng"@en ; ns0:peerReviewStatus "Unreviewed"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "Banff International Research Station for Mathematical Innovation and Discovery"@en ; dcterms:rights "Attribution-NonCommercial-NoDerivatives 4.0 International"@en ; ns0:rightsURI "http://creativecommons.org/licenses/by-nc-nd/4.0/"@en ; ns0:scholarLevel "Faculty"@en ; dcterms:isPartOf "BIRS Workshop Lecture Videos (Oaxaca de Juárez (Mexico))"@en ; dcterms:subject "Mathematics"@en, "Combinatorics"@en, "Group theory and generalizations"@en, "Discrete mathematics"@en ; dcterms:title "Symmetry Breaking"@en ; dcterms:type "Moving Image"@en ; ns0:identifierURI "http://hdl.handle.net/2429/68822"@en .