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ON AXIOMS OF BIQUANDLES
Preview AbstractWe prove that the two conditions from the definition of a biquandle by Fenn, Jordan-Santana, Kauffman [1] are equivalent and thus answer a question posed in the paper. We also construct a weak biquandle, which is not a biquandle.
BIQUANDLE LONGITUDE INVARIANT OF LONG VIRTUAL KNOTS
Preview AbstractIt is known that the number of biquandle colorings of a long virtual knot diagram, with a fixed color of the initial arc, is a knot invariant. In this paper, we construct a more subtle invariant: a family of biquandle endomorphisms obtained from the set of colorings and longitudinal information.