Matrices and finite biquandles
By Sam Nelson, J. Vo. 2006
47 citations recorded by the source corpus.
Wedescribeawayofrepresentingfinitebiquandleswithnelements as 2n ◊ 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 nontrivialityofthevirtualtrefoilandvariousKishinoknots.Wealso exhibitanorientedvirtualknotwhichisdistinguishedfromboth its obverse and its reverse by a finite biquandle counting invariant.Weclassifybiquandlesoforder2,3and4andprovideaURL for our Maple programs for computing with finite biquandles.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4df301e8dceac3e3757680ae3baa797c2cabdbd8
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The structure of medial quandles (2014, methodology): “ McCarron calculated the numbers in the first two rows for n≤ 9, and in the third row for n≤ 10, see OEIS sequences A181769, A165200, A178432 [20] (no reference is given there). Earlier, Ho and Nelson [9] enumerated quandles up to size 8, by an exhaustive search over all permutations that fill the row”
- On Structure Groups of Set-Theoretic Solutions to the Yang–Baxter Equation (2017, unknown): “Such solutions are used for producing efficient colouring invariants of knots and their higher-dimensional analogues: see [16,29,31] and references therein.”