A Rewriting Approach to Graph Invariants

Lars Hellström ()

Chapter 5 in Generalized Lie Theory in Mathematics, Physics and Beyond, 2009, pp 47-67 from Springer

Abstract: 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”.

Keywords: Monoidal Category; Internal Edge; Diagrammatic Calculation; External Edge; Spin Network (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-85332-9_5

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DOI: 10.1007/978-3-540-85332-9_5

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