The Online Journal of Undergraduate Papers in Knot Theory

The OJUPKT is a non-refereed collection of papers written by undergraduates in the field of knot theory. The goal of the OJUPKT is to provide a resource where undergraduates interested in knot theory can find papers written by their peers.

The OJUPKT lists two types of papers: First, papers that have not yet been published in a journal can be accepted here for publication and will be hosted on this website. Second, we also provide links to papers that have been published elsewhere. Links will point either to the journal itself, or to one of the authors' home sites.

Submission Guidelines

  • Papers can be about any aspect of knot theory.

  • Every submission must be sponsored by a faculty member.

  • Send all submissions to Laura Taalman at taal@math.jmu.edu.

  • A complete submission consists of:
    • A list of all authors of the paper.
    • The title of the paper and the year it was completed.
    • The name and email address of a faculty sponsor/advisor.
    • The name of the institution where the research was done.
    • The name of any program or REU that was involved.
    • If submitting to the OJPUKT for publication, include an electronic copy of the paper, in PDF format.
    • If submitting to the OJPUKT as a link, include a web address that points to the full text of the paper.


Undergraduate Papers in Knot Theory

On the Harary-Kauffman Conjecture and Turk's Head Knots (link to arXiv)
  • Authors: Nicholas Dowdall, Thomas Mattman, Kevin Meek, and Pablo Solis
  • Faculty Advisor: Thomas Mattman
  • Venue: Chico State REUT and NREUP sites
  • Year: 2006
Colorability and determinants of T(m,n,r,s) twisted torus knots for n ≡ +/- 1 (mod m) (link to preprint)
  • Authors: Matt DeLong, Matthew Russell, and Jonathan Schrock
  • Faculty Advisor: Matt DeLong
  • Venue: Taylor University, Step Grant
  • Year: 2008
Intrinsic knotting of bipartite graphs (pdf file)
  • Authors: Sophy Huck, Alexandra Appel, and Miguel-Angel Manrique
  • Faculty Advisor: Thomas Mattman
  • Venue: NSF REU at California State University, Chico
  • Year: 2007
Intrinsic knotting of partite graphs (pdf file)
  • Authors: Chloe Collins, Ryan Hake, Cara Petonic, and Laura Sardanga
  • Faculty Advisor: Thomas Mattman
  • Venue: Joint NSF REUT/SUMMA summer research program, California State University, Chico
  • Year: 2006
p-Colorings of Weaving Knots (pdf file)
  • Author: Layla Oesper
  • Faculty Advisor: Sandy Ganzell
  • Venue: Pomona College
  • Year: 2005
Intrinsic knotting and linking of almost complete graphs (link to arXiv)
  • Authors: Jesse Campbell, Thomas Mattman, Ryan Ottman, Joel Pyzer, Matthew Rodrigues, and Sam Williams
  • Faculty Advisor: Thomas Mattman
  • Venue: Joint NSF REUT/SUMMA summer research program, California State University, Chico
  • Year: 2005
Boundary slope diameter and crossing number of 2-bridge knots (link to arXiv)
  • Authors: Thomas Mattman, Gabriel Maybrun, and Kristin Robinson
  • Faculty Advisor: Thomas Mattman
  • Venue: Joint NSF REUT/SUMMA summer research program, California State University, Chico
  • Year: 2005
Intrinic knotting and linking of almost complete partite graphs (link to arXiv)
  • Authors: Thomas Mattman, Ryan Ottman, and Matt Rodrigues
  • Faculty Advisor: Thomas Mattman
  • Venue: Joint NSF REUT/SUMMA summer research program, California State University, Chico
  • Year: 2004
Bounds on the crosscap numbers of torus knots (link to arXiv)
  • Authors: Thomas Mattman and Owen Sizemore
  • Faculty Advisor: Thomas Mattman
  • Venue: Joint NSF REUT/SUMMA summer research program, California State University, Chico
  • Year: 2004
Ribbonlength of torus knots (link to arXiv)
  • Authors: Brooke Brennan, Thomas Mattman, Roberto Raya, and Dan Tating
  • Faculty Advisor: Thomas Mattman
  • Venue: Joint NSF REUT/SUMMA summer research program, California State University, Chico
  • Year: 2004
Torus links and the bracket polynomial (pdf file)
  • Author: Paul Corbitt
  • Faculty Advisor: Michael McLendon
  • Venue: Washington College
  • Year: 2004
p-Coloring classes of torus knots (pdf file)
  • Authors: Anna-Lisa Breiland and Layla Oesper
  • Faculty Advisor: Laura Taalman
  • Venue: Summer REU program, James Madison University
  • Year: 2004
k-Alternating knots (link to pdf of preprint)
  • Published in Topology and its Applications Volume 150, Issues 1-3, 14 May 2005, Pages 125-131 (link)
  • Authors: Philip Hackney and Nathan Walters
  • Faculty Advisor: Leonard Van Wyk
  • Venue: Summer REU Program, James Madison University
  • Year: 2003 (published 2005)
Coloring invariant and determinants (pdf file)
  • Author: Candice Price
  • Faculty Advisor: Thomas Mattman
  • Venue: SUMMA summer research program, California State University, Chico
  • Year: 2003
Using link invariants to determine shapes for links (pdf file)
  • Author: Dan Tating
  • Faculty Advisor: Thomas Mattman
  • Venue: SUMMA summer research program, California State University, Chico
  • Year: 2003
The Alexander polynomial, coloring, and determinants of knots (pdf file)
  • Author: Raquel Lopez
  • Faculty Advisor: Thomas Mattman
  • Venue: SUMMA summer research program, California State University, Chico
  • Year: 2003
Fundamentally different m-colorings of pretzel knots (pdf file)
  • Authors: Kathryn Brownell and Kaitlyn O'Neil
  • Faculty Advisor: Laura Taalman
  • Venue: Summer REU program, James Madison University
  • Year: 2003