We introduce an algebraic structure we call semiquandles whose axioms are derived from flat Reidemeister moves. Finite semiquandles have associated counting invariants and enhanced invariants defined for flat virtual knots and links. We also introduce singular semiquandles and virtual singular semiquandles which define…
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3 results for “semiquandle”
An example of semiquandle and u-polynomials for flat virtual knots via this semiquandle coloringmath.GT
The paper introduces a semiquandle for flat virtual knots and connects it to u-polynomials.
problem Defining invariants for flat virtual knots.
method Developed a semiquandle and used it to define an invariant for flat virtual knots.
result The semiquandle invariant relates to u-polynomials for flat virtual knots.
A birack is an algebraic structure with axioms encoding the blackboard-framed Reidemeister moves, incorporating quandles, racks, strong biquandles and semiquandles as special cases. In this paper we extend the counting invariant for finite racks to the case of finite biracks. We introduce a family of biracks generalizi…