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A chord diagram expansion coming from some Dyson-Schwinger equations

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arxiv 1210.5457 v1 pith:EZGNXKG4 submitted 2012-10-19 math.CO math-phmath.MP

Nicolas Marie , Karen Yeats This is my paper · ORCID
classification math.COmath-phmath.MP
keywords chordconnecteddiagramsdyson-schwingerequationsexpansiongiverooted
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We give an expression for the solution to propagator-type Dyson-Schwinger equations with one primitive at 1 loop as an expansion over rooted connected chord diagrams. Along the way we give a refinement of a classical recurrence of rooted connected chord diagrams, and a representation in terms of binary trees.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The algebraic structure of Dyson--Schwinger equations with multiple insertion places

    math.CO 2025-01 conditional novelty 5.0 of 10

    Provides tubing-expansion solutions to Dyson-Schwinger equations with multiple insertion places, and proves one conjecture of Nabergall while disproving another.

  2. On the Relation of Exact Hydrodynamics to the Chapman-Enskog Series

    math-ph 2025-06 conditional novelty 4.0 of 10

    For a one-dimensional BGK kinetic model, the Chapman-Enskog expansion is a local Taylor approximation to the exact spectral hydrodynamic mode and diverges for every nonzero wave number, while the spectral closure rema...

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