109 citations · 289 across the 23 of their papers we have counts for
11 papers · 1 filter
On determinants of resistance matrices
Harry Richman, Farbod Shokrieh, Chenxi Wu
We prove a new combinatorial identity for the determinant of the resistance matrix of a finite graph, which involves counts of spanning trees and forests. This generalizes a result…
Principal minors of tree distance matrices
Harry Richman, Farbod Shokrieh, Chenxi Wu
We prove that the principal minors of the distance matrix of a tree satisfy a combinatorial expression involving counts of rooted spanning forests of the underlying tree. This gene…
Counting two-forests and random cut size via potential theory
Harry Richman, Farbod Shokrieh, Chenxi Wu
We prove a lower bound on the number of spanning two-forests in a graph, in terms of the number of vertices, edges, and spanning trees. This implies an upper bound on the average c…
Torsor Structures on Spanning Trees
Farbod Shokrieh, Cameron Wright
We study two actions of the (degree 0) Picard group on the set of the spanning trees of a finite ribbon graph. It is known that these two actions, denoted and respectiv…
Metric graphs, cross ratios, and Rayleigh's laws
Robin de Jong, Farbod Shokrieh
We study a notion of cross ratios on metric graphs and electrical networks. We show that several known results immediately follow from the basic properties of cross ratios. We show…
Divisors on graphs, binomial and monomial ideals, and cellular resolutions
Fatemeh Mohammadi, Farbod Shokrieh
We study various binomial and monomial ideals arising in the theory of divisors, orientations, and matroids on graphs. We use ideas from potential theory on graphs and from the the…
Canonical representatives for divisor classes on tropical curves and the Matrix-Tree Theorem
Yang An, Matthew Baker, Greg Kuperberg +1
Let be a compact tropical curve (or metric graph) of genus . Using the theory of tropical theta functions, Mikhalkin and Zharkov proved that there is a canonical effective r…
Divisors on graphs, Connected flags, and Syzygies
Fatemeh Mohammadi, Farbod Shokrieh
We study the binomial and monomial ideals arising from linear equivalence of divisors on graphs from the point of view of Gröbner theory. We give an explicit description of a minim…
Chip-firing games, potential theory on graphs, and spanning trees
Matthew Baker, Farbod Shokrieh
We study the interplay between chip-firing games and potential theory on graphs, characterizing reduced divisors (-parking functions) on graphs as the solution to an energy (or…
The monodromy pairing and discrete logarithm on the Jacobian of finite graphs
Farbod Shokrieh
Every graph has a canonical finite abelian group attached to it. This group has appeared in the literature under a variety of names including the sandpile group, critical group, Ja…
Chip-Firing Games, -Parking Functions, and an Efficient Bijective Proof of the Matrix-Tree Theorem
Farbod Shokrieh
Kirchhoff's matrix-tree theorem states that the number of spanning trees of a graph G is equal to the value of the determinant of the reduced Laplacian of . We outline an effici…