Hello Bruce, > I am now reading Chapter I of Lando and Zvonkin so I > have a much better idea of your interests.
Cool! But beyond ramified covers of the sphere (as in [LZ]) and Strebel differentials (as in the paper [MP] mentioned by Tom), I used ribbon graph as a topological object : a graph embedded in a surface. In particular they define a simplicial structure from which we may define a complex with a derivation which gives homology groups of the surface (as well as Poincare duality). The latter is the main part of what I have implemented and from which I'm able to compute what is called the spin-parity of a translation surface (see [KZ]) which depends only on some angle data between each half-edge. > I allow boundary points which I have not seen; > but you did mention partial permutations. I will > have a look at your code and see if I can figure > out what you have implemented. In a sense I do not allow boundary point, but it depends on what you mean by boundary point. Every permutation I consider are defined on a subset of {0,1,...,n} and I call it partial if the domain (which equals the range) is not {0,1,...,n}. The terminology I used is perhaps misleading... In your definition, a boundary point correspond a half-edge which is not glued to another half-edge, isn't it ? But, you can think of it as a fixed point for the involution defining the edges. My question is does the other two permutations (the vertex permutation and face permutation) are well defined on these boundary points ? In other words, does these half-edges are embedded in the surface ? [LZ] Lando, Zvonkine, "Graphs on Surfaces and Their Applications", Springer [MP] Mulase, Penkava, http://arxiv.org/abs/math-ph/9811024 [KZ] Kontsevich,Zorich, http://arxiv.org/abs/math/0201292 Best, Vincent -- You received this message because you are subscribed to the Google Groups "sage-combinat-devel" group. To post to this group, send email to sage-combinat-devel@googlegroups.com. To unsubscribe from this group, send email to sage-combinat-devel+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sage-combinat-devel?hl=en.