Generalized polynomial invariants for virtual knots via parity
Abstract
By extending the quiver state model that calculates the generalized Alexander polynomial defined by Kauffman and Radford, we introduce a new state model via the parity for crossings and define a polynomial called the even generalized Alexander polynomial in the paper. We prove that this polynomial is an invariant of virtual knots and show that there is a specific virtual knot that can be distinguished from the trivial knot by the polynomial. We introduce other generalized polynomial invariants via parity.
Fields of Study & Subjects
Geometric and Algebraic Topology
Advanced Graph Theory Research
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Journal of Knot Theory and Its Ramifications
- Volume
- 35
- Issue
- 11
- Publication date
- 12 February 2026
- Language
- EN