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Questions about the Tutte polynomial of graphs and matroids, which is a polynomial in two variables encoding many interesting combinatorial informations.
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Number of spanning subgraphs of $K_n$ with given number of edges and connected components
Given some positive integers $n,e$ and $c$, I would like to know the number of spanning subgraphs of $K_n$ having $e$ edges and $c$ connected components.
Essentially, what I am asking for here is …