Geodesic
The algebra of bipartite graphs and Hurwitz numbers of seamed surfaces
Izvestiya. Mathematics , Tome 72 (2008) no. 4, pp. 627-646

Voir la notice de l'article provenant de la source Math-Net.Ru

We extend the definition of Hurwitz numbers to the case of seamed surfaces, which arise in new models of mathematical physics, and prove that they form a system of correlators for a Klein topological field theory in the sense defined in [1]. We find the corresponding Cardy–Frobenius algebras, which yield a method for calculating the Hurwitz numbers. As a by-product, we prove that the vector space generated by the bipartite graphs with $n$ edges possesses a natural binary operation that makes this space into a non-commutative Frobenius algebra isomorphic to the algebra of intertwining operators for a representation of the symmetric group $S_n$ on the space generated by the set of all partitions of a set of $n$ elements. 
@article{IM2_2008_72_4_a0,
     author = {A. V. Alekseevskii and S. M. Natanzon},
     title = {The algebra of bipartite graphs and {Hurwitz} numbers of seamed surfaces},
     journal = {Izvestiya. Mathematics },
     pages = {627--646},
     publisher = {mathdoc},
     volume = {72},
     number = {4},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2008_72_4_a0/}
}
TY  - JOUR
AU  - A. V. Alekseevskii
AU  - S. M. Natanzon
TI  - The algebra of bipartite graphs and Hurwitz numbers of seamed surfaces
JO  - Izvestiya. Mathematics 
PY  - 2008
SP  - 627
EP  - 646
VL  - 72
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2008_72_4_a0/
LA  - en
ID  - IM2_2008_72_4_a0
ER  - 
%0 Journal Article
%A A. V. Alekseevskii
%A S. M. Natanzon
%T The algebra of bipartite graphs and Hurwitz numbers of seamed surfaces
%J Izvestiya. Mathematics 
%D 2008
%P 627-646
%V 72
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2008_72_4_a0/
%G en
%F IM2_2008_72_4_a0
A. V. Alekseevskii; S. M. Natanzon. The algebra of bipartite graphs and Hurwitz numbers of seamed surfaces. Izvestiya. Mathematics , Tome 72 (2008) no. 4, pp. 627-646. http://geodesic.mathdoc.fr/item/IM2_2008_72_4_a0/