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Combinatorial Classes and Rooted Trees

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A Combinatorial Perspective on Quantum Field Theory

Part of the book series: SpringerBriefs in Mathematical Physics ((BRIEFSMAPHY,volume 15))

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Abstract

This chapter gives an overview of combinatorial classes and their generating functions with a focus on rooted trees and the connection between combinatorial specifications and Dyson-Schwinger equations.

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Notes

  1. 1.

    The loop order , rephrased in graph theory language, is the dimension of the cycle space of the graph, see Sect. 5.5. In topological language this is the first Betti number. Loop in Feynman diagram language means cycle in graph theory language; the graph theorist’s loops are called tadpoles or self-loops.

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Authors and Affiliations

  1. Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada

    Karen Yeats

  2. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, Canada

    Karen Yeats

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  1. Karen Yeats
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Correspondence to Karen Yeats .

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Yeats, K. (2017). Combinatorial Classes and Rooted Trees. In: A Combinatorial Perspective on Quantum Field Theory. SpringerBriefs in Mathematical Physics, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-319-47551-6_3

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