Zobrazeno 1 - 10
of 133
pro vyhledávání: '"Dye, H."'
Autor:
Chrisman, Micah W., Dye, H. A.
This paper introduces two virtual knot theory ``analogues'' of a well-known family of invariants for knots in thickened surfaces: the Grishanov-Vassiliev finite-type invariants of order two. The first, called the three loop isotopy invariant, is an i
Externí odkaz:
http://arxiv.org/abs/1309.2971
Autor:
Dye, H. A.
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 knots. One family consists of degree $n$ Vassiliev invariants.
Comm
Comm
Externí odkaz:
http://arxiv.org/abs/1203.2939
Autor:
Dye, H. A.
We construct two knot invariants. The first knot invariant is a sum constructed using linking numbers. The second is an invariant of flat knots and is a formal sum of flat knots obtained by smoothing pairs of crossings. This invariant can be used in
Externí odkaz:
http://arxiv.org/abs/1109.3165
Autor:
Dye, H. A.
We explore a family of invariants obtained from linking numbers. This is a family of Kauffman finite type invariants.
Comment: 14 pages, 20 figures
Comment: 14 pages, 20 figures
Externí odkaz:
http://arxiv.org/abs/1007.1175
We investigate relationships between bounds on the crossing number and the mosaic number of mosaic knots.
Comment: 10 pages, 13 figures, This paper details the work completed during a Research Experience for Undergraduates at McKendree Universit
Comment: 10 pages, 13 figures, This paper details the work completed during a Research Experience for Undergraduates at McKendree Universit
Externí odkaz:
http://arxiv.org/abs/1004.2214
Autor:
Dye, H. A., Kauffman, Louis H.
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.
Comment: 14 pages, 23 figures
Comment: 14 pages, 23 figures
Externí odkaz:
http://arxiv.org/abs/0909.1672
We compute lower bounds on the virtual crossing number and minimal surface genus of virtual knot diagrams from the arrow polynomial. In particular, we focus on several interesting examples.
Comment: 17 Pages, 18 figures and 7 tables
Comment: 17 Pages, 18 figures and 7 tables
Externí odkaz:
http://arxiv.org/abs/0904.1525
Autor:
Dye, H. A., Kauffman, Louis H.
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.
Comment: 28 pages, 35 figures v2: Updated bibliography and Soulie kn
Comment: 28 pages, 35 figures v2: Updated bibliography and Soulie kn
Externí odkaz:
http://arxiv.org/abs/0810.3858
Autor:
Dye, H. A.
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 changes. We recall the pure virtual braid group. We then describe the set of
Externí odkaz:
http://arxiv.org/abs/0704.3089
Autor:
Dye, H. A., Kauffman, Louis H.
Two welded (respectively virtual) link diagrams are homotopic if one may be transformed into the other by a sequence of extended Reidemeister moves, classical Reidemeister moves, and self crossing changes. In this paper, we extend Milnor's mu and bar
Externí odkaz:
http://arxiv.org/abs/math/0611076