6 citations · 27 across the 20 of their papers we have counts for
9 papers · 1 filter
Ribbon decomposition and twisted Hurwitz numbers
Yurii Burman, Raphaël Fesler
Ribbon decomposition is a way to obtain a surface with boundary (compact, not necessarily oriented) from a collection of disks by joining them with narrow ribbons attached to segme…
Lie elements and the matrix-tree theorem
Yurii Burman, Valeriy Kulishov
For a finite-dimensional representation V of a group G we introduce and study the notion of a Lie element in the group algebra k[G]. The set L(V) \subset k[G] of Lie elements is a…
Abstract matrix-tree theorem and Bernardi polynomial
Yurii Burman
This paper is a continuation of arXiv:1612.03873. We prove a three-parameter family of identities (Theorem 1.1) involving a version of the Tutte polynomial for directed graphs intr…
Abstract matrix-tree theorem
Yurii Burman
The classical matrix-tree theorem discovered by G.Kirchhoff in 1847 relates the principal minor of the nxn Laplace matrix to a particular sum of monomials of matrix elements indexe…
Higher determinants and the matrix-tree theorem
Yurii Burman
The classical matrix-tree theorem was discovered by G.~Kirchhoff in 1847. It relates the principal minor of the Laplace (nxn)-matrix to a particular sum of monomials indexed by the…
Operators of rank 1, discrete path integration and graph Laplacians
Yurii M. Burman
We prove a formula for a characteristic polynomial of an operator expressed as a polynomial of rank 1 operators. The formula uses a discrete analog of path integration and implies…
Higher matrix-tree theorems
Yurii Burman, Andrey Ploskonosov, Anastasia Trofimova
We calculate determinants of weighted sums of reflections and of (nested) commutators of reflections. The results obtained generalize the Kirchhoff's matrix-tree theorem and the ma…
Around matrix-tree theorem
Yurii Burman, Boris Shapiro
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 m…
Parking functions and Haglund--Loehr data
Yurii M. Burman
A parking function is a sequence of N nonnegative integers majorated by a permutation of the set {0, ..., N-1}. We provide a way to encode parking functions by data suggested by J.…