7 citations · 10 across the 19 of their papers we have counts for
24 papers
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…
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 merge trees with a given homological sequence
Nicholas A. Scoville, Dylan Wen
In this paper, we study the induced homological sequence and the induced merge tree of a discrete Morse function on a tree. A discrete Morse function on a tree gives rise to a sequ…
A McCord-type theorem for pseudotopological spaces and directed graphs
Nikola Milićević, Nicholas A. Scoville
We construct weak homotopy equivalences between the geometric realizations of directed Vietoris-Rips complexes and their underlying directed graphs, seen as pseudotopological space…
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…
A Second Homotopy Group for Digital Images
Gregory Lupton, Oleg Musin, Nicholas A. Scoville +2
We define a second (higher) homotopy group for digital images. Namely, we construct a functor from digital images to abelian groups, which closely resembles the ordinary second hom…