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Generalizing the classical matrix-tree theorem we provide a formula counting subgraphs of a given graph with a fixed 2-core. We use this generalization to obtain an analog of the matrix-tree theorem for the root system Dn (the classical theorem corresponds to the An-case). Several byproducts of the developed technique, such as a new formula for a(More)
Fixing an arbitrary point p ∈ CP 2 and a triple (g, d,) of non-negative integers satisfying the inequality g ≤ d+l−1 2 − l 2 , we associate a natural Hurwitz number to the (open) Severi-type variety W g,d,, consisting of all reduced irreducibke plane curves of degree d + l with genus g and having an ordinary singularity of order l at p (the remaining(More)
The article contains a generalization of the classical Whit-ney formula for the number of double points of a plane curve. This formula is split into a series of equalities, and also extended to curves on a torus, to non-pointed curves, and to wave fronts. All the theorems are given geometric proofs employing logarithmic Gauss-type maps from suitable(More)
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