Corpus ID: 119603125

Several graph sequences as solutions of a double recurrence

  title={Several graph sequences as solutions of a double recurrence},
  author={Christian Brouder and William J. Keith and {\^A}ngela Mestre},
  journal={arXiv: Combinatorics},
We describe the combinatorics that arise in summing a double recursion formula for the enumeration of connected Feynman graphs in quantum field theory. In one index the problem is more tractable and yields concise formulas which are combinatorially interesting on their own. In the other index, one of these sums is Sloane's sequence A001865. 


Generating loop graphs via Hopf algebra in quantum field theory
We use the Hopf algebra structure of the time-ordered algebra of field operators to generate all connected weighted Feynman graphs in a recursive and efficient manner. The algebraic representation ofExpand
A Note on the Symmetric Powers of the Standard Representation of Sn
In this paper, we prove that the dimension of the space span- ned by the characters of the symmetric powers of the standard $n$-dimensional representation of $S_n$ is asymptotic to $n^2 / 2$. This isExpand
Depth-First Search as a Combinatorial Correspondence
Abstract A depth first search algorithm is used to establish the connection between labeled connected graphs and inversions of trees.
The On-Line Encyclopedia of Integer Sequences
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