Matches in SemOpenAlex for { <https://semopenalex.org/work/W2922255736> ?p ?o ?g. }
Showing items 1 to 55 of
55
with 100 items per page.
- W2922255736 abstract "In this thesis we present two new applications of the representation theory of finite groups in discrete mathematics. The first application is in coding theory. We further develop the theory of upper bounds for error-correcting codes and mixed binary/ternary codes, thereby expanding upon the work of Gijswijt et al. and Brouwer et al. We consider semidefinite programs based on quadruples of codewords and apply a symmetry reduction to obtain an optimization problem of polynomial size. This enables us to solve the semidefinite program with the aid of the computer for several values of n (the length of the words), q (the size of the alphabet) and d (the distance). The second application of representation theory is concerned with the enumeration of local flows in embedded graphs. We extend the domain of the surface Tutte polynomial of Goodall et al. to include non-orientable embedded graphs and show that this invariant for embedded graphs contains for every finite group G the number of nowhere-identity local G-flows and the number of nowhere-identity local G-tensions as evaluations. We prove that for an embedded graph nowhere-identity local tensions correspond with proper colorings of a covering of the embedded graph, thereby generalizing coloring-flow duality for planar graphs. The surface Tutte polynomial also specializes to a trivariate polynomial for signed graphs. We show that this polynomial has a universal property, which we finally use to give combinatorial interpretations of several of its evaluations." @default.
- W2922255736 created "2019-03-22" @default.
- W2922255736 creator A5024966830 @default.
- W2922255736 date "2019-01-01" @default.
- W2922255736 modified "2023-09-27" @default.
- W2922255736 title "Applications of representation theory in discrete mathematics" @default.
- W2922255736 hasPublicationYear "2019" @default.
- W2922255736 type Work @default.
- W2922255736 sameAs 2922255736 @default.
- W2922255736 citedByCount "0" @default.
- W2922255736 crossrefType "journal-article" @default.
- W2922255736 hasAuthorship W2922255736A5024966830 @default.
- W2922255736 hasConcept C113709454 @default.
- W2922255736 hasConcept C114614502 @default.
- W2922255736 hasConcept C118615104 @default.
- W2922255736 hasConcept C132525143 @default.
- W2922255736 hasConcept C14447369 @default.
- W2922255736 hasConcept C203776342 @default.
- W2922255736 hasConcept C22149727 @default.
- W2922255736 hasConcept C33923547 @default.
- W2922255736 hasConceptScore W2922255736C113709454 @default.
- W2922255736 hasConceptScore W2922255736C114614502 @default.
- W2922255736 hasConceptScore W2922255736C118615104 @default.
- W2922255736 hasConceptScore W2922255736C132525143 @default.
- W2922255736 hasConceptScore W2922255736C14447369 @default.
- W2922255736 hasConceptScore W2922255736C203776342 @default.
- W2922255736 hasConceptScore W2922255736C22149727 @default.
- W2922255736 hasConceptScore W2922255736C33923547 @default.
- W2922255736 hasLocation W29222557361 @default.
- W2922255736 hasOpenAccess W2922255736 @default.
- W2922255736 hasPrimaryLocation W29222557361 @default.
- W2922255736 hasRelatedWork W1475836543 @default.
- W2922255736 hasRelatedWork W1506968473 @default.
- W2922255736 hasRelatedWork W1516961187 @default.
- W2922255736 hasRelatedWork W1560723985 @default.
- W2922255736 hasRelatedWork W162015597 @default.
- W2922255736 hasRelatedWork W187003101 @default.
- W2922255736 hasRelatedWork W2065259354 @default.
- W2922255736 hasRelatedWork W2067653823 @default.
- W2922255736 hasRelatedWork W2078293958 @default.
- W2922255736 hasRelatedWork W2123114890 @default.
- W2922255736 hasRelatedWork W2171778703 @default.
- W2922255736 hasRelatedWork W2269054999 @default.
- W2922255736 hasRelatedWork W2550386713 @default.
- W2922255736 hasRelatedWork W2606302946 @default.
- W2922255736 hasRelatedWork W2758407290 @default.
- W2922255736 hasRelatedWork W2770854599 @default.
- W2922255736 hasRelatedWork W2900288768 @default.
- W2922255736 hasRelatedWork W2962684356 @default.
- W2922255736 hasRelatedWork W2995995989 @default.
- W2922255736 hasRelatedWork W3130122773 @default.
- W2922255736 isParatext "false" @default.
- W2922255736 isRetracted "false" @default.
- W2922255736 magId "2922255736" @default.
- W2922255736 workType "article" @default.