Geodesic
Matrices and finite biquandles
Homology, homotopy, and applications, Tome 8 (2006) no. 2, pp. 51-73.

Voir la notice de l'article provenant de la source International Press of Boston

We describe away of representing finite biquandles with $n$ elements as $2n \times 2n$ block matrices. Any finite biquandle defines an invariant of virtual knots through counting homomorphisms. The counting invariants of non-quandle biquandles can reveal information not present in the knot quandle, such as the nontriviality of the virtual trefoil and various Kishino knots. We also exhibit an oriented virtual knot which is distinguished from both its obverse and its reverse by a finite biquandle counting invariant. We classify biquandles of order 2, 3 and 4 and provide a URL for our Maple programs for computing with finite biquandles.
DOI : 10.4310/HHA.2006.v8.n2.a3
Classification : 57M25, 57M27
Keywords: finite biquandles, virtual knot invariants 
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Sam Nelson; John Vo. Matrices and finite biquandles. Homology, homotopy, and applications, Tome 8 (2006) no. 2, pp. 51-73. doi : 10.4310/HHA.2006.v8.n2.a3. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2006.v8.n2.a3/

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