All word pairs over two free generators that make every group a birack or biquandle are classified, and new union, product, holomorph, and covering constructions for biquandles are introduced with their automorphism groups.
From biquandle structures to Hom-biquandles
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abstract
We investigate the relationship between the quandle and biquandle coloring invariant and obtain an enhancement of the quandle and biquandle coloring invariants using biquandle structures. We also continue the study of biquandle homomorphisms into a medial biquandle begun by the second author et al., finding biquandle analogs of results about Hom-quandles. We describe the biquandle structure of the Hom-biquandle, and consider the relationship between the Hom-quandle and Hom-biquandle.
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math.GR 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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General constructions of biquandles and their symmetries
All word pairs over two free generators that make every group a birack or biquandle are classified, and new union, product, holomorph, and covering constructions for biquandles are introduced with their automorphism groups.