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A Rewriting Approach to Graph Invariants
Mälardalen University, School of Education, Culture and Communication. Umeå University. (Mathematics/Applied Mathematics)ORCID iD: 0000-0001-6140-180X
2009 (English)In: Generalized Lie Theory in Mathematics, Physics and Beyond / [ed] Sergei Silvestrov, Eugen Paal, Viktor Abramov, Alexander Stolin, Berlin, Heidelberg: Springer, 2009, p. 47-67Chapter in book (Refereed)
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”.

Place, publisher, year, edition, pages
Berlin, Heidelberg: Springer, 2009. p. 47-67
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-24093DOI: 10.1007/978-3-540-85332-9_5ISBN: 978-3-540-85331-2 (print)ISBN: 978-3-540-85332-9 (print)OAI: oai:DiVA.org:mdh-24093DiVA, id: diva2:682978
Available from: 2013-12-31 Created: 2013-12-31 Last updated: 2015-06-29Bibliographically approved

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Publisher's full texthttp://link.springer.com/chapter/10.1007/978-3-540-85332-9_5

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Hellström, Lars

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  • nn-NB
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