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Annales de l’Institut Henri Poincaré D

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Volume 2, Issue 4, 2015, pp. 413–430
DOI: 10.4171/AIHPD/22

Published online: 2015-11-14

Tree hook length formulae, Feynman rules and B-series

Bradley R. Jones[1] and Karen Yeats[2]

(1) Simon Fraser University, Burnaby, Canada
(2) Simon Fraser University, Burnaby, Canada

We consider weighted generating functions of trees where the weights are products of functions of the sizes of the subtrees. This work begins with the observation that three different communities, largely independently, found substantially the same result concerning these series. We unify these results with a common generalization. Next we use the insights of one community on the problems of another in two different ways. Namely, we use the differential equation perspective to find a number of new interesting hook length formulae for trees, and we use the body of examples developed by the combinatorial community to give quantum field theory toy examples with nice properties.

Keywords: Trees, tree hook length, tree Dyson–Schwinger equations

Jones Bradley, Yeats Karen: Tree hook length formulae, Feynman rules and B-series. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 2 (2015), 413-430. doi: 10.4171/AIHPD/22