30 citations · 184 across the 89 of their papers we have counts for
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An isomorphism theorem for Alexander biquandles
Daisy Lam, Sam Nelson
We show that two Alexander biquandles M and M' are isomorphic iff there is an isomorphism of Z[s,1/s,t,1/t]-modules h:(1-st)M --> (1-st)M' and a bijection g:O_s(A) --> O_s(A') betw…
Quandles and Linking Number
Natasha Harrell, Sam Nelson
We study the quandle counting invariant for a certain family of finite quandles with trivial orbit subquandles. We show how these invariants determine the linking number of classic…
Matrices and Finite Biquandles
Sam Nelson, John Vo
We describe a way of representing finite biquandles with n elements as 2n x 2n block matrices. Any finite biquandle defines an invariant of virtual knots through counting homomorph…
Non-classicality and quandle difference invariants
Natasha Harrell, Sam Nelson
Non-classical virtual knots may have non-isomorphic upper and lower quandles. We exploit this property to define the quandle difference invariant, which can detect non-classicality…