Spencer Backman

Partial graph orientations and the Tutte polynomial

Gessel and Sagan investigated the Tutte polynomial,

Infinite reduction of divisors on metric graphs

T(x,y)

Chip-firing via open covers

using depth first search, and applied their techniques to show that the number of acyclic partial orientations of a graph is

Sum-product inequalities with perturbation

2^gT(3,1/2)

Riemann–Roch theory for graph orientations

. We provide a short deletion-contraction proof of this result and demonstrate that dually, the number of strongly connected partial orientations is

Chip-Firing and Riemann-Roch Theory for Directed Graphs

2^{n-1}T(1/2,3)

Fourientation activities and the Tutte polynomial

. We then prove that the number of partial orientations modulo cycle reversals is

Fourientations and the Tutte polynomial

2^gT(3,1)

A convolution formula for Tutte polynomials of arithmetic matroids and other combinatorial structures

and the number of partial orientations modulo cut reversals is

A Bijection Between the Recurrent Configurations of a Hereditary Chip-Firing Model and Spanning Trees

2^{n-1}T(1,3)