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A Rewriting Approach to Graph Invariants
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation. Umeå University. (Mathematics/Applied Mathematics)ORCID-id: 0000-0001-6140-180X
2009 (engelsk)Inngår i: Generalized Lie Theory in Mathematics, Physics and Beyond / [ed] Sergei Silvestrov, Eugen Paal, Viktor Abramov, Alexander Stolin, Berlin, Heidelberg: Springer, 2009, s. 47-67Kapittel i bok, del av antologi (Fagfellevurdert)
Abstract [en]

Diagrammatic calculation is a powerful tool that gets near indispensable when one tries to manage some of the newer algebraic structures that have been popping up in the last couple of decades. Concretely, it generalises the underlying structure of expressions to being general graphs, where traditional algebraic notation only supports path- or treelike expressions. This paper demonstrates how to apply the author's Generic Diamond Lemma in diagrammatic calculations, by solving through elementary rewriting techniques the problem of classifying all multigraph invariants satisfying a linear contract—delete recursion. (As expected, this leads one to rediscover the Tutte polynomial, along with some more degenerate invariants.) In addition, a concept of “semigraph” is defined which formalises the concept of a graph-theoretical “gadget”.

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Berlin, Heidelberg: Springer, 2009. s. 47-67
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matematik/tillämpad matematik
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URN: urn:nbn:se:mdh:diva-24093DOI: 10.1007/978-3-540-85332-9_5ISBN: 978-3-540-85331-2 (tryckt)ISBN: 978-3-540-85332-9 (tryckt)OAI: oai:DiVA.org:mdh-24093DiVA, id: diva2:682978
Tilgjengelig fra: 2013-12-31 Laget: 2013-12-31 Sist oppdatert: 2015-06-29bibliografisk kontrollert

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