9 citations
5 papers
Factorization Properties of Leamer Monoids
Jason Haarmann, Ashlee Kalauli, Aleesha Moran +2
The Huneke-Wiegand conjecture has prompted much recent research in Commutative Algebra. In studying this conjecture for certain classes of rings, García-Sánchez and Leamer construc…
Vassiliev Invariants from Parity Mappings
H. A. Dye
Parity mappings from the chords of a Gauss diagram to the integers is defined. The parity of the chords is used to construct families of invariants of Gauss diagrams and virtual kn…
Anyonic Topological Quantum Computation and the Virtual Braid Group
H. A. Dye, Louis H. Kauffman
We introduce a recoupling theory for virtual braided trees. This recoupling theory can be utilized to incorporate swap gates into anyonic models of quantum computation.
Virtual Crossing Number and the Arrow Polynomial
H. A. Dye, Louis H. Kauffman
We introduce a new polynomial invariant of virtual knots and links and use this invariant to compute a lower bound on the virtual crossing number and the minimal surface genus.
Pure Virtual Braids Homotopic to the Identity Braid
H. A. Dye
Two virtual link diagrams are homotopic if one may be transformed into the other by a sequence of virtual Reidemeister moves, classical Reidemeister moves, and self crossing change…