4 papers
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…
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…
Maximum Persistent Betti Numbers of Äech Complexes
Herbert Edelsbrunner, Matthew Kahle, Shu Kanazawa
This note proves that only a linear number of holes in a Äech complex of points in can persist over an interval of constant length. Specifically, for any fixed…
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…