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Séminaire Lotharingien de Combinatoire, B61An (2011), 37 pp.

# William G. Faris

# Combinatorial Species and Feynman Diagrams

**Abstract.**
A Feynman diagram is a graphical construction
that describes certain interactions in physics.
Most calculations with such diagrams reduce to consideration of connected
Feynman diagrams. These in turn may be constructed from
line-irreducible Feynman diagrams, those for which removal
of a single line does not destroy connectivity. The purpose of
this article is to exhibit the combinatorial nature of
this construction in the framework of species of structures.
The main result is a dissymmetry theorem for connected Feynman diagrams.
This purely combinatorial theorem relates the species of connected diagrams to
species with less symmetry, such as the species of connected
diagrams with a designated line-irreducible subdiagram.
There is also a discussion of the relation of this result to the
Legendre transform.

Received: May 17, 2010.
Revised: January 4, 2011; June 1, 2011.
Accepted: June 17, 2011.

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