Communications in Number Theory and Physics

Volume 7 (2013)

Number 2

A chord diagram expansion coming from some Dyson-Schwinger equations

Pages: 251 – 291

DOI: http://dx.doi.org/10.4310/CNTP.2013.v7.n2.a2

Authors

Nicolas Marie (Department of Mathematics, Simon Fraser University, Burnaby, B.C., Canada)

Karen Yeats (Department of Mathematics, Simon Fraser University, Burnaby, B.C., Canada)

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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