Matches in SemOpenAlex for { <https://semopenalex.org/work/W4367060675> ?p ?o ?g. }
Showing items 1 to 61 of
61
with 100 items per page.
- W4367060675 abstract "Bidirected graphs are directed multigraphs admitting arrows having two starting or two ending points. With arbitrary such graph we associate a non-negative integral quadratic form as a so-called incidence form. We show that each non-negative form of Dynkin type A, D or C arises in this way, and that all certain roots of an integral quadratic form come from walks in the associated bidirected graph. We show that these results yield useful tools to prove new facts and to perform efficient computations for integral quadratic forms and related problems in number theory, algebra and graph theory. Among others, we prove the universality property for a large class of integral quadratic forms; we provide computational methods to find solutions or to characterize the finiteness of the sets of solutions of various related Diophantine equations; we show a variant of Whitney's theorem on line graphs using switching classes, and that reflections through mentioned roots can be realized as switching; we generalize known classification of non-negative quadratic forms of Dynkin types A and D (with respect to the usual Z-equivalence as well as the Gabrielov equivalence) to type C. Moreover, we apply our techniques to give a conceptual and constructive proof of the non-negativity and the possible Dynkin types of the Euler quadratic forms of a class of finite-dimensional gentle algebras." @default.
- W4367060675 created "2023-04-27" @default.
- W4367060675 creator A5022224215 @default.
- W4367060675 creator A5044846856 @default.
- W4367060675 date "2023-04-24" @default.
- W4367060675 modified "2023-09-27" @default.
- W4367060675 title "Bidirected graphs, integral quadratic forms and some Diophantine equations" @default.
- W4367060675 doi "https://doi.org/10.48550/arxiv.2304.12555" @default.
- W4367060675 hasPublicationYear "2023" @default.
- W4367060675 type Work @default.
- W4367060675 citedByCount "0" @default.
- W4367060675 crossrefType "posted-content" @default.
- W4367060675 hasAuthorship W4367060675A5022224215 @default.
- W4367060675 hasAuthorship W4367060675A5044846856 @default.
- W4367060675 hasBestOaLocation W43670606751 @default.
- W4367060675 hasConcept C111919701 @default.
- W4367060675 hasConcept C114614502 @default.
- W4367060675 hasConcept C118615104 @default.
- W4367060675 hasConcept C129844170 @default.
- W4367060675 hasConcept C166437778 @default.
- W4367060675 hasConcept C195392725 @default.
- W4367060675 hasConcept C202444582 @default.
- W4367060675 hasConcept C202854965 @default.
- W4367060675 hasConcept C206530611 @default.
- W4367060675 hasConcept C2524010 @default.
- W4367060675 hasConcept C2778701210 @default.
- W4367060675 hasConcept C33923547 @default.
- W4367060675 hasConcept C41008148 @default.
- W4367060675 hasConcept C80695182 @default.
- W4367060675 hasConcept C98045186 @default.
- W4367060675 hasConceptScore W4367060675C111919701 @default.
- W4367060675 hasConceptScore W4367060675C114614502 @default.
- W4367060675 hasConceptScore W4367060675C118615104 @default.
- W4367060675 hasConceptScore W4367060675C129844170 @default.
- W4367060675 hasConceptScore W4367060675C166437778 @default.
- W4367060675 hasConceptScore W4367060675C195392725 @default.
- W4367060675 hasConceptScore W4367060675C202444582 @default.
- W4367060675 hasConceptScore W4367060675C202854965 @default.
- W4367060675 hasConceptScore W4367060675C206530611 @default.
- W4367060675 hasConceptScore W4367060675C2524010 @default.
- W4367060675 hasConceptScore W4367060675C2778701210 @default.
- W4367060675 hasConceptScore W4367060675C33923547 @default.
- W4367060675 hasConceptScore W4367060675C41008148 @default.
- W4367060675 hasConceptScore W4367060675C80695182 @default.
- W4367060675 hasConceptScore W4367060675C98045186 @default.
- W4367060675 hasLocation W43670606751 @default.
- W4367060675 hasOpenAccess W4367060675 @default.
- W4367060675 hasPrimaryLocation W43670606751 @default.
- W4367060675 hasRelatedWork W1490568884 @default.
- W4367060675 hasRelatedWork W158287491 @default.
- W4367060675 hasRelatedWork W1972129239 @default.
- W4367060675 hasRelatedWork W1986717972 @default.
- W4367060675 hasRelatedWork W2005971232 @default.
- W4367060675 hasRelatedWork W201195458 @default.
- W4367060675 hasRelatedWork W2032906403 @default.
- W4367060675 hasRelatedWork W2089408657 @default.
- W4367060675 hasRelatedWork W2619453705 @default.
- W4367060675 hasRelatedWork W2772529464 @default.
- W4367060675 isParatext "false" @default.
- W4367060675 isRetracted "false" @default.
- W4367060675 workType "article" @default.