172 citations · 377 across the 33 of their papers we have counts for
43 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…
Random chain complexes of real vector spaces
Ayat Ababneh, Matthew Kahle
We introduce a natural class of models of random chain complexes of real vector spaces that some classical ensembles of random matrices, the length case. We are interested here…
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…
Maximum Persistent Betti Numbers of Čech Complexes
Herbert Edelsbrunner, Matthew Kahle, Shu Kanazawa
This note proves that only a linear number of holes in a Čech complex of points in can persist over an interval of constant length. Specifically, for any fixed d…
Maximal persistence in random clique complexes
Ayat Ababneh, Matthew Kahle
We study the persistent homology of an Erdős--Rényi random clique complex filtration on vertices. Here, each edge appears at a time chosen uniform randomly…
On the clique number of noisy random geometric graphs
Matthew Kahle, Minghao Tian, Yusu Wang
Let be a random geometric graph, and then for we construct a "-perturbed noisy random geometric graph" where each existing edge in is…