FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2617504623> ?p ?o ?g. }

• W2617504623 abstract "Let Sn be the symmetric group on [n] = {1,. . . ,n}. The k-point fixing graph, F(n, k) isdefined to be the graph with vertex set Sn and two vertices g and h of F(n, k) are joinedif and only if gh−1 fixes exactly k points. F(n, k) is a Cayley graph on Sn generated byS (n, k), the union of the conjugacy classes that fixes exactly k points. A subset I of Sn issaid to be an independent set in F(n, k) if and only if any two vertices in I are not adjacentto each other. The problem of finding such a set is called the maximum independent setproblem and it is an NP-hard optimization problem. We are going to determine the sizeof the largest independent set in F(n, k) for 0 < k << n by using the Delsarte-HoffmanBound. In order to do so, eigenvalues of the adjacency matrix of F(n, k) are required infinding a bound for the size of a largest independent set in F(n, k).To determine the eigenvalues of the adjacency matrix of F(n, k), we use the representationtheory of symmetric groups. In particular, we use the character theory of symmetricgroups. We apply the branching rule and results from Foulkes to derive a recurrenceformula for eigenvalues of F(n, k). Then we apply our results and some of the resultsregarding the eigenvalues and size of largest independent set of F(n,0) to determinethe sign of the eigenvalues of F(n,1). Then, we determine the smallest eigenvalue ofF(n,1) by techniques in extremal combinatorics. We use the largest and smallest eigenvaluesof F(n,1) and apply the Delsarte-Hoffman Bound to determine a bound for thesize of a largest independent set in F(n,1). When 0 < k << n, we determine the smallesteigenvalues of F(n, k) and the Specht module where it occurs. Similarly, we use thelargest and smallest eigenvalues of F(n, k) and apply the Delsarte-Hoffman Bound todetermine a bound for the size of a largest independent set in F(n, k).We also consider F(n,0), the derangement graph with generating set Dn, the derangementset. For any fixed positive integer k ≤ n, the Cayley graph on Sn generated by thesubset of Dn consisting of permutations without any i-cycles for all 1 ≤ i ≤ k is a regularsubgraph of the derangement graph. We determine the smallest eigenvalue of these subgraphsand show that the set of all largest independent sets in these subgraphs is equal tothe set of all the largest independent sets in F(n,0) provided that k << n.h" @default.
• W2617504623 created "2017-06-05" @default.
• W2617504623 creator A5058176227 @default.
• W2617504623 date "2016-12-05" @default.
• W2617504623 modified "2023-09-24" @default.
• W2617504623 title "On eigenvalues of certain cayley graphs / Terry Lau Shue Chien" @default.
• W2617504623 hasPublicationYear "2016" @default.
• W2617504623 type Work @default.
• W2617504623 sameAs 2617504623 @default.
• W2617504623 citedByCount "0" @default.
• W2617504623 crossrefType "dissertation" @default.
• W2617504623 hasAuthorship W2617504623A5058176227 @default.
• W2617504623 hasConcept C114614502 @default.
• W2617504623 hasConcept C118615104 @default.
• W2617504623 hasConcept C120204988 @default.
• W2617504623 hasConcept C121332964 @default.
• W2617504623 hasConcept C128622974 @default.
• W2617504623 hasConcept C132525143 @default.
• W2617504623 hasConcept C158693339 @default.
• W2617504623 hasConcept C180356752 @default.
• W2617504623 hasConcept C33923547 @default.
• W2617504623 hasConcept C62520636 @default.
• W2617504623 hasConcept C80899671 @default.
• W2617504623 hasConceptScore W2617504623C114614502 @default.
• W2617504623 hasConceptScore W2617504623C118615104 @default.
• W2617504623 hasConceptScore W2617504623C120204988 @default.
• W2617504623 hasConceptScore W2617504623C121332964 @default.
• W2617504623 hasConceptScore W2617504623C128622974 @default.
• W2617504623 hasConceptScore W2617504623C132525143 @default.
• W2617504623 hasConceptScore W2617504623C158693339 @default.
• W2617504623 hasConceptScore W2617504623C180356752 @default.
• W2617504623 hasConceptScore W2617504623C33923547 @default.
• W2617504623 hasConceptScore W2617504623C62520636 @default.
• W2617504623 hasConceptScore W2617504623C80899671 @default.
• W2617504623 hasLocation W26175046231 @default.
• W2617504623 hasOpenAccess W2617504623 @default.
• W2617504623 hasPrimaryLocation W26175046231 @default.
• W2617504623 hasRelatedWork W1919156896 @default.
• W2617504623 hasRelatedWork W1965754865 @default.
• W2617504623 hasRelatedWork W1980290091 @default.
• W2617504623 hasRelatedWork W1993433103 @default.
• W2617504623 hasRelatedWork W2008726491 @default.
• W2617504623 hasRelatedWork W2025323123 @default.
• W2617504623 hasRelatedWork W2042608907 @default.
• W2617504623 hasRelatedWork W2059272542 @default.
• W2617504623 hasRelatedWork W2131966829 @default.
• W2617504623 hasRelatedWork W2242573402 @default.
• W2617504623 hasRelatedWork W2278042759 @default.
• W2617504623 hasRelatedWork W2311581783 @default.
• W2617504623 hasRelatedWork W2410952847 @default.
• W2617504623 hasRelatedWork W2603304008 @default.
• W2617504623 hasRelatedWork W2949155560 @default.
• W2617504623 hasRelatedWork W2949635812 @default.
• W2617504623 hasRelatedWork W2950388741 @default.
• W2617504623 hasRelatedWork W3099080852 @default.
• W2617504623 hasRelatedWork W3106160126 @default.
• W2617504623 hasRelatedWork W3203098167 @default.
• W2617504623 isParatext "false" @default.
• W2617504623 isRetracted "false" @default.
• W2617504623 magId "2617504623" @default.
• W2617504623 workType "dissertation" @default.