publications

publications by categories in reversed chronological order. generated by jekyll-scholar.

2026

  1. The sequential star matching on the Vietoris-Rips complex
    Pawel Dlotko, Julian Brüggemann, and Nicholas A. Scoville
    2026
    in preparation
  2. A Lusternik–Schnirelmann theorem using collapsible covers
    Julian Brüggemann, David Mosquera-Lois, and Nicholas A. Scoville
    2026
    in preparation
  3. Generalized gradient vector fields and the complex of discrete Morse intervals
    Nicholas A. Scoville
    2026
    submitted
    Code
  4. The complex of discrete Morse matchings of the n-simplex: homotopy types and structural results
    Nicholas A. Scoville
    2026
    submitted
    Code
  5. The Face Group of a Simplicial Complex
    Gregory Lupton, Nicholas A. Scoville, and P. Christopher Staecker
    2026
    submitted
  6. Summation graphs and discrete Morse theory
    Dominic Klyve and Nicholas A. Scoville
    2026
    submitted
  7. A McCord-type theorem for pseudotopological spaces and directed graphs
    Nikola Milićević and Nicholas A. Scoville
    Journal of Applied and Computational Topology, 2026
    DOI
  8. Discrete Morse theory for open complexes
    Kevin P. Knudson and Nicholas A. Scoville
    Topology and its Applications, 2026
    DOI

2025

  1. On cycles and merge trees
    Julian Brüggemann and Nicholas A. Scoville
    Journal of Pure and Applied Algebra, 2025

2024

  1. A Second Homotopy Group for Digital Images
    Gregory Lupton, Oleg Musin, Nicholas A. Scoville, and 2 more authors
    Journal of Algebraic Combinatorics, 2024
    DOI

2023

  1. Star clusters in the Matching, Morse, and Generalized complex of discrete Morse functions
    Connor Donovan and Nicholas A. Scoville
    New York Journal of Mathematics, 2023
  2. The Closure Operation as the Foundation of Topology: A Mini-Primary Source Project for Topology Students
    Nicholas A. Scoville
    Convergence, Jun 2023
  3. The digital Hopf construction
    Gregory Lupton, John Oprea, and Nicholas A. Scoville
    Topology and its Applications, 2023
    DOI

2022

  1. Merge trees in discrete Morse theory
    Benjamin Johnson and Nicholas A. Scoville
    Research in the Mathematical Sciences, 2022
    DOI
  2. Digital Fundamental Groups and Edge Groups of Clique Complexes
    Gregory Lupton and Nicholas A. Scoville
    Journal of Applied and Computational Topology, 2022
    DOI
  3. Fundamental Theorems of Morse theory on posets
    Desamparados Fernandez-Ternero, Enrique Macias-Virgos, David Mosquera-Lois, and 2 more authors
    AIMS Mathematics, 2022
    DOI
  4. Subdivision of Maps of Digital Images
    Gregory Lupton, John Oprea, and Nicholas A. Scoville
    Discrete and Computational Geometry, 2022
    DOI
  5. Higher connectivity of the Morse complex
    Nicholas A. Scoville and Matthew C. B. Zaremsky
    Proceedings of the American Mathematical Society, Series B, 2022
  6. On the homotopy and strong homotopy type of complexes of discrete Morse functions
    Connor Donovan, Maxwell Lin, and Nicholas A. Scoville
    Canadian Mathematical Bulletin, 2022
    DOI
  7. Homotopy Theory in Digital Topology
    Gregory Lupton, John Oprea, and Nicholas A. Scoville
    Discrete and Computational Geometry, 2022
    DOI

2021

  1. On the Automorphism group of the Morse complex
    Maxwell Lin and Nicholas A. Scoville
    Advances in Applied Mathematics, 2021
    DOI
  2. A Fundamental Group for Digital Images
    Gregory Lupton, John Oprea, and Nicholas A. Scoville
    Journal of Applied and Computational Topology, 2021
    DOI

2020

  1. Topology from Analysis: A Mini-Primary Source Project for Topology Students
    Nicholas A. Scoville
    Convergence, Jun 2020
  2. Strong discrete Morse theory and simplicial Lusternik–Schnirelmann category: A discrete version of the Lusternik-Schnirelmann Theorem
    Desamparados Fernandez-Ternero, Enrique Macias-Virgos, Nicholas A. Scoville, and 1 more author
    Discrete and Computational Geometry, 2020
    DOI
  3. Discrete Morse functions, vector fields, and homological sequences on trees
    Ian Rand and Nicholas A. Scoville
    Involve, a Journal of Mathematics, 2020
    DOI
  4. The realization problem for discrete Morse functions on trees
    Yuqing Liu and Nicholas A. Scoville
    Algebra Colloquium, 2020
    DOI

2019

  1. The Cantor Set Before Cantor: A Mini-Primary Source Project for Analysis and Topology Students
    Nicholas A. Scoville
    Convergence, May 2019
  2. Homological sequences in discrete Morse theory
    Mike Agiorgousis, Brian Green, Alex Onderdonk, and 2 more authors
    Topology Proceedings, 2019
  3. Knots Related by Knotoids
    Colin Adams, Allison Henrich, Kate Kearney, and 1 more author
    American Mathematical Monthly, 2019
    DOI

2017

  1. A Persistent Homological Analysis of Network Data Flow Malfunctions
    Nicholas A. Scoville and Karthik Yegnesh
    Journal of Complex Networks, 2017
    DOI
  2. Connecting Connectedness: A Mini-Primary Source Project for Topology Students
    Nicholas A. Scoville
    Convergence, Oct 2017
  3. On the Lusternik–Schnirelmann category of a simplicial map
    Nicholas A. Scoville and Willie Swei
    Topology and its Applications, 2017

2015

  1. Estimating the discrete Lusternik–Schnirelmann category
    Brian Green, Nicholas A. Scoville, and Mimi Tsuruga
    Topological Methods in Nonlinear Analysis, 2015

2014

  1. A Distributed Greedy Algorithm for Constructing Connected Dominating Sets in Wireless Sensor Networks
    Akshaye Dhawan, Michelle Tanco, and Nicholas A. Scoville
    In SENSORNETS, Jan 2014
  2. Metric Structures for CW Complexes
    Nicholas A. Scoville
    Topology Proceedings, 2014
  3. Graph Isomorphisms in discrete Morse theory
    Seth Aaronson, Marie Meyer, Nicholas A. Scoville, and 2 more authors
    AKCE International Journal of Graphs and Combinatorics, 2014

2013

  1. Lusternik–Schnirelmann category for cell complexes
    Seth Aaronson and Nicholas A. Scoville
    Illinois Journal of Mathematics, 2013

2012

  1. Georg Cantor at the Dawn of Point-Set Topology
    Nicholas A. Scoville
    Loci, Mar 2012
    DOI
  2. Lusternik–Schnirelmann Category and the Connectivity of X
    Nicholas A. Scoville
    Algebraic & Geometric Topology, 2012

2011

  1. Mapping Cone Sequences and a Generalized Notion of Cone Length
    Nicholas A. Scoville
    JP Journal of Geometry and Topology, 2011

2010

  1. A Metric for Homotopy Types
    Nicholas A. Scoville
    Dartmouth College, 2010

2006

  1. Categorical Sequences
    Rob Nendorf, Nicholas A. Scoville, and Jeff Strom
    Algebraic & Geometric Topology, 2006