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- YURII BURMAN
- 2005

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)

- YURII BURMAN
- 2014

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)

Consider factorizations into transpositions of an n-cycle in the symmetric group S n. To every such factorization we assign a mono-mial in variables w ij that retains the transpositions used, but forgets their order. Summing over all possible factorizations of n-cycles we obtain a polynomial that happens to admit a closed expression. From this expression we… (More)

Consider factorizations into transpositions of an n-cycle in the symmetric group S n. To every such factorization we assign a mono-mial in variables w ij that retains the transpositions used, but forgets their order. Summing over all possible factorizations of n-cycles we obtain a polynomial that happens to admit a closed expression. From this expression we… (More)

- YURII BURMAN
- 2004

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)

We introduce a new class of admissible pairs of triangular sequences and prove a bijection between the set of admissible pairs of triangular sequences of length n and the set of parking functions of length n. For all u and v = 0, 1, 2, 3 and all n ≤ 7 we describe in terms of admissible pairs the dimensions of the bi-graded components h u,v of diagonal… (More)

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