no. 4
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
Keywords: Trees, tree hook length, tree Dyson–Schwinger equations 
@article{AIHPD_2015__2_4_413_0,
     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},
     pages = {413--430},
     year = {2015},
     volume = {2},
     number = {4},
     doi = {10.4171/aihpd/22},
     language = {en},
     url = {https://www.numdam.org/articles/10.4171/aihpd/22/}
}
TY  - JOUR
AU  - Jones, Bradley R.
AU  - Yeats, Karen
TI  - Tree hook length formulae, Feynman rules and B-series
JO  - Annales de l’Institut Henri Poincaré D
PY  - 2015
SP  - 413
EP  - 430
VL  - 2
IS  - 4
UR  - https://www.numdam.org/articles/10.4171/aihpd/22/
DO  - 10.4171/aihpd/22
LA  - en
ID  - AIHPD_2015__2_4_413_0
ER  - 
%0 Journal Article
%A Jones, Bradley R.
%A Yeats, Karen
%T Tree hook length formulae, Feynman rules and B-series
%J Annales de l’Institut Henri Poincaré D
%D 2015
%P 413-430
%V 2
%N 4
%U https://www.numdam.org/articles/10.4171/aihpd/22/
%R 10.4171/aihpd/22
%G en
%F AIHPD_2015__2_4_413_0
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

Cité par Sources :