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A direct proof of the Harer-Zagier recursion enumerating the ways to paste a 2n-gon to get a genus g surface?
In a 1986 paper, Harer and Zagier proved the recursion:
$$(n+1)e(g,n)=(4n-2)e(g,n-1)+(2n-1)(n-1)(2n-3)e(g-1,n-2)$$
where e(g,n) is the number of ways of grouping sides $S_1...S_{2n}$ of a 2n-gon ...
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Reference for the image of the adjoint to the differential in graph cohomology (which yields STU & IHX)?
One can define cochain complexes of (combinatorial) graphs, where each term is a vector space of linear combinations of certain (isomorphism classes of) graphs, and where the differential $d$ is a ...
