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2006 Matrices and finite biquandles
Sam Nelson, John Vo
Homology Homotopy Appl. 8(2): 51-73 (2006).

Abstract

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.

Citation

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Sam Nelson. John Vo. "Matrices and finite biquandles." Homology Homotopy Appl. 8 (2) 51 - 73, 2006.

Information

Published: 2006
First available in Project Euclid: 5 April 2007

zbMATH: 1111.57009
MathSciNet: MR2246021

Subjects:
Primary: 57M25, 57M27

Rights: Copyright © 2006 International Press of Boston

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Vol.8 • No. 2 • 2006
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