Provides tubing-expansion solutions to Dyson-Schwinger equations with multiple insertion places, and proves one conjecture of Nabergall while disproving another.
A chord diagram expansion coming from some Dyson-Schwinger equations
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abstract
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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The algebraic structure of Dyson--Schwinger equations with multiple insertion places
Provides tubing-expansion solutions to Dyson-Schwinger equations with multiple insertion places, and proves one conjecture of Nabergall while disproving another.