12 citations · 16 across the 7 of their papers we have counts for
7 papers
High-dimensional holeyominoes
Greg Malen, Fedor Manin, Erika Roldan
What is the maximum number of holes enclosed by a -dimensional polyomino built of tiles? Represent this number by . Recent results show that converges to…
Topology and Geometry of Crystallized Polyominoes
Greg Malen, Érika Roldán
We give a complete solution to the extremal topological combinatorial problem of finding the minimum number of tiles needed to construct a polyomino with holes. We denote this…
Moduli Spaces of Morse Functions for Persistence
Michael J. Catanzaro, Justin Curry, Brittany Terese Fasy +5
We consider different notions of equivalence for Morse functions on the sphere in the context of persistent homology, and introduce new invariants to study these equivalence classe…
Polyiamonds Attaining Extremal Topological Properties, Part II
Greg Malen, Érika Roldán
In Part II of this work, we construct crystallized polyiamonds with holes for every , that is polyiamonds which use the fewest possible tiles necessary to enclose ho…
Collapsibility of Random Clique Complexes
Greg Malen
We prove a sufficient condition for a finite clique complex to collapse to a -dimensional complex, and use this to exhibit thresholds for -collapsibility in a sparse rand…
Homomorphism Complexes and k-Cores
Greg Malen
We prove that the topological connectivity of a graph homomorphism complex Hom() is at least , where . This is a strong…