4 citations · 5 across the 4 of their papers we have counts for
4 papers
A Lattice-Theoretic Perspective on the Persistence Map
Brendan Mallery, Adélie Garin, Justin Curry
We provide a naturally isomorphic description of the persistence map from merge trees to barcodes in terms of a monotone map from the partition lattice to the subset lattice. Our d…
Houghton-like groups from "shift-similar" groups
Brendan Mallery, Matthew C. B. Zaremsky
We introduce and study \emph{shift-similar} groups , which play an analogous role in the world of Houghton groups that self-similar groups play in the…
From Trees to Barcodes and Back Again II: Combinatorial and Probabilistic Aspects of a Topological Inverse Problem
Justin Curry, Jordan DeSha, Adélie Garin +3
In this paper we consider two aspects of the inverse problem of how to construct merge trees realizing a given barcode. Much of our investigation exploits a recently discovered con…
Medium-scale curvature at larger radii in finitely generated groups
Robert Kropholler, Brendan Mallery
In this paper we study medium scale curvature, a notion of Ricci curvature for groups. We show that dead-end elements yield non-negative curvature. We make use of related elements…