5 papers · 1 filter
The complex of discrete Morse matchings of the -simplex: homotopy types and structural results
Nicholas A. Scoville
The complex of discrete Morse matchings $\M(K)$, introduced by Chari and Joswig, is a simplicial complex whose simplices are the acyclic matchings on the Hasse diagram of . Its…
Discrete Morse theory for open complexes
Kevin P. Knudson, Nicholas A. Scoville
We develop a discrete Morse theory for open simplicial complexes where is a simplicial complex and a subcomplex of . A discrete Morse function on $K…
The Face Group of a Simplicial Complex
Gregory Lupton, Nicholas A. Scoville, P. Christopher Staecker
The edge group of a simplicial complex is a well-known, combinatorial version of the fundamental group. It is a group associated to a simplicial complex that consists of equivalenc…
On cycles and merge trees
Julian Brüggemann, Nicholas A. Scoville
In this paper, we extend the notion of a merge tree to that of a generalized merge tree, a merge tree that includes 1-dimensional cycle birth information. Given a discrete Morse fu…
The directed Vietoris-Rips complex and homotopy and singular homology groups of finite digraphs
Nikola MiliÄeviÄ, Nicholas A. Scoville
We prove analogues of classical results for higher homotopy groups and singular homology groups of pseudotopological spaces. Pseudotopological spaces are a generalization of (Äech…