1 citations · 2 across the 3 of their papers we have counts for
6 papers
On the Orbit Decomposition of Finite Quandles
Sam Nelson, Chau-Yim Wong
We study the structure of finite quandles in terms of subquandles. Every finite quandle decomposes in a natural way as a union of disjoint -complemented subquandles; this de…
Matrices and Finite Quandles
Benita Ho, Sam Nelson
Finite quandles with n elements can be represented as n-by-n matrices. We show how to use these matrices to distinguish all isomorphism classes of finite quandles for a given cardi…
Virtual Crossing Realization
Sam Nelson
We study virtual isotopy sequences with classical initial and final diagrams, asking when such a sequence can be changed into a classical isotopy sequence by replacing virtual cros…
Classification of Finite Alexander Quandles
Sam Nelson
Two finite Alexander quandles with the same number of elements are isomorphic iff their Z[t,t^-1]-submodules Im(1-t) are isomorphic as modules. This yields specific conditions on w…
The Betti numbers of some finite racks
R. A. Litherland, Sam Nelson
We show that the lower bounds for Betti numbers given in math.GT/9909161 are equalities for a class of racks that includes dihedral and Alexander racks. We confirm a conjecture fro…
Unknotting virtual knots with Gauss diagram forbidden moves
Sam Nelson
The forbidden moves can be combined with Gauss diagram Reidemeister moves to obtain move sequences with which we may change any Gauss diagram (and hence any virtual knot) into any…