Combinatorical and Algebraic Structures Seminar

Session details

Date: 25.3.2008
Speaker: Angela Mestre, Doppler Institute
Title: The combinatorics of connected graphs and a Hopf algebraic representation of graphs
Abstract: We present a recursion formula to efficiently generate all connected graphs. This formula is restricted subsequently to 1-particle irreducible graphs and to connected graphs without self-loops. All graphs are generated together with weights given by the inverses of their symmetry factors. The recursions proceed by loop order and vertex number. Furthermore, we introduce an algebraic representation of graphs based on the Hopf algebra structure of the algebra of quantum field operators. We derive an algebraic expression for the aforesaid recurrence, so as to generate all connected graphs directly in this representation. Our approach leads to efficient algorithms suitable for concrete computations.

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