Combinatorics of rooted trees and Hopf algebras
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Publication:4417289
DOI10.1090/S0002-9947-03-03317-8zbMath1048.16023arXivmath/0201253MaRDI QIDQ4417289
Publication date: 28 July 2003
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0201253
Trees (05C05) Perturbative methods of renormalization applied to problems in quantum field theory (81T15)
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Uses Software
Cites Work
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- Hopf-algebraic structure of families of trees
- Generalized Robinson-Schensted-Knuth correspondence
- Hopf algebras, renormalization and noncommutative geometry
- On the Hopf algebra strucutre of perturbative quantum field theories
- Hopf algebras, cyclic cohomology and the transverse index theorem
- Renormalization automated by Hopf algebra
- Duality of graded graphs
- Schensted algorithms for dual graded graphs
- Relating the Connes-Kreimer and Grossman-Larson Hopf algebras built on rooted trees
- On overlapping divergences
- Finite dimensional comodules over the Hopf algebra of rooted trees
- On the structure of Hopf algebras
- Differential Posets
- Knots and Feynman Diagrams
- Ordered structures and partitions
- Chen's iterated integral represents the operator product expansion
- An analogue of covering space theory for ranked posets