172 citations · 377 across the 33 of their papers we have counts for
14 papers · 1 filter
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…
A combinatorial genesis of the right-angled relations in Artin's classical braid groups
Omar Alvarado-Garduño, Jesús González, Matthew Kahle
The configuration space of unlabelled non-overlapping unit squares in a rectangle is known to recover the homotopy type of the classical co…
Asymptotic Betti numbers for hard squares in the homological liquid regime
Hannah Alpert, Matthew Kahle, Robert MacPherson
We study configuration spaces of ordered unit squares in a by rectangle. Our goal is to estimate the Betti numbers for large , , , and . We con…
Homology of configuration spaces of hard squares in a rectangle
Hannah Alpert, Ulrich Bauer, Matthew Kahle +2
We study ordered configuration spaces of hard squares in a rectangle, a generalization of the well-known "15 Puzzle". Our main interest is in the topolo…
Topology and geometry of random 2-dimensional hypertrees
Matthew Kahle, Andrew Newman
A hypertree, or -acyclic complex, is a higher-dimensional analogue of a tree. We study random -dimensional hypertrees according to the determinantal measure suggeste…
Configuration spaces of disks in an infinite strip
Hannah Alpert, Matthew Kahle, Robert MacPherson
We study the topology of the configuration spaces of hard disks of unit diameter in an infinite strip of width . We describe ranges of parameter or "regimes", where…