Affiliation:
1. McKendree University, 701 College Road, Lebanon IL 62254, USA
Abstract
We construct two knot invariants. The first knot invariant is a matrix constructed using linking numbers. This matrix can be represented as a two variable polynomial. 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 conjunction with other flat invariants, forming a family of invariants. Both invariants are constructed using the parity of a crossing.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
5 articles.
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1. Intersection formulas for parities on virtual knots;Journal of Knot Theory and Its Ramifications;2023-04
2. The Wriggle polynomial for virtual tangles;Journal of Knot Theory and Its Ramifications;2019-12
3. Linking invariants;An Invitation to Knot Theory;2018-09-03
4. The three loop isotopy and framed isotopy invariants of virtual knots;Topology and its Applications;2014-08
5. VASSILIEV INVARIANTS FROM PARITY MAPPINGS;Journal of Knot Theory and Its Ramifications;2013-04