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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