Alex Kontorovich

collaborators

4 papers

math.CO2025

Effective resistance in planar graphs and continued fractions

Swee Hong Chan, Alex Kontorovich, Igor Pak

For a simple graph $G = (V, E)$ and edge $e \in E$ , the effective resistance is defined as a ratio $\frac{τ ( G / e )}{τ ( G )}$ , where $τ (G)$ denotes the number of spanning trees in $G$ . We r…

math.CO2024

Spanning trees and continued fractions

Swee Hong Chan, Alex Kontorovich, Igor Pak

We prove the exponential growth of the cardinality of the set of numbers of spanning trees in simple (and planar) graphs on $n$ vertices, answering a question of Sedláček from 1969…

math.NT2024

On the Local-Global Conjecture for Combinatorial Period Lengths of Closed Billiards on the Regular Pentagon

Alex Kontorovich, Xin Zhang

We study the set of combinatorial lengths of asymmetric periodic trajectories on the regular pentagon, proving a density-one version of a conjecture of Davis-Lelievre.

math.NT2024

Lax-Phillips orbit counting in higher rank

Alex Kontorovich, Christopher Lutsko

Given a discrete lattice, $Γ < SL_{m} (R)$ , and a base point $o \in R^{m}$ , let $N_{Γ} (T)$ denote the number of points in the orbit $o \cdot Γ$ whose (Eucl…