4 papers
The 15 Puzzle and homological stability in the space direction
Jesús González, Matthew Kahle, Nicholas Wawrykow
The ordered configuration space of open unit squares in the by rectangle exhibits homological stability in the space direction. That is, for fixed and fixed homolog…
Representation asymptotics in the homology of pure graph braid groups
Louis Hainaut, Ben Knudsen, Nicholas Wawrykow
We give explicit formulas for the asymptotic Betti numbers, over an arbitrary field, of the ordered configuration spaces of a graph. In characteristic zero, we further give explici…
Chip-firing on trees of loops
Sameer Kailasa, Vivian Kuperberg, Nicholas Wawrykow
Cools, Draisma, Payne, and Robeva proved that generic metric graphs that are "paths of loops" are Brill-Noether general. We show that Brill-Noether generality does not hold for "tr…
Realization of groups with pairing as Jacobians of finite graphs
Louis Gaudet, David Jensen, Dhruv Ranganathan +2
We study which groups with pairing can occur as the Jacobian of a finite graph. We provide explicit constructions of graphs whose Jacobian realizes a large fraction of odd groups w…