Tree hook length formulae, Feynman rules and B-series
Annales de l’Institut Henri Poincaré D, Tome 2 (2015) no. 4, pp. 413-430.

We consider weighted generating functions of trees where the weights are products of functions of the sizes of the subtrees. Th�is work begins with the observation that three di�fferent 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 di�fferent ways. Namely, we use the di�fferential 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.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/22
Classification : 05-XX, 81-XX
Mots-clés : Trees, tree hook length, tree Dyson–Schwinger equations 
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     author = {Jones, Bradley R. and Yeats, Karen},
     title = {Tree hook length formulae, {Feynman} rules and {B-series}},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
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     volume = {2},
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     language = {en},
     url = {http://archive.numdam.org/articles/10.4171/aihpd/22/}
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Jones, Bradley R.; Yeats, Karen. Tree hook length formulae, Feynman rules and B-series. Annales de l’Institut Henri Poincaré D, Tome 2 (2015) no. 4, pp. 413-430. doi : 10.4171/aihpd/22. http://archive.numdam.org/articles/10.4171/aihpd/22/

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