Geodesic
On the genus distribution of \((p,q,n)\)-dipoles
The electronic journal of combinatorics, Tome 14 (2007)
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There are many applications of the enumeration of maps in surfaces to other areas of mathematics and the physical sciences. In particular, in quantum field theory and string theory, there are many examples of occasions where it is necessary to sum over all the Feynman graphs of a certain type. In a recent paper of Constable et al. on pp-wave string interactions, they must sum over a class of Feynman graphs which are equivalent to what we call $(p,q,n)$-dipoles. In this paper we perform a combinatorial analysis that gives an exact formula for the number of $(p,q,n)$-dipoles in the torus (genus 1) and double torus (genus 2).
DOI : 10.37236/930
Classification : 05C30, 05A15, 05C10
Mots-clés : Feynman graphs, enumeration of maps in surfaces 
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     author = {Terry I. Visentin and Susana W. Wieler},
     title = {On the genus distribution of \((p,q,n)\)-dipoles},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/930},
     zbl = {1114.05049},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/930/}
}
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Terry I. Visentin; Susana W. Wieler. On the genus distribution of \((p,q,n)\)-dipoles. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/930

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