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Symmetric Enhancements of Involutory Virtual Birack Counting Invariants
Melinda Ho, Sam Nelson
We consider involutory virtual biracks with good involutions, also known as symmetric involutory virtual biracks. Any good involution on an involutory virtual birack defines an enh…
Bikei Invariants and Gauss Diagrams for Virtual Knotted Surfaces
Sam Nelson, Patricia Rivera
Marked vertex diagrams provide a combinatorial way to represent knotted surfaces in ; including virtual crossings allows for a theory of virtual knotted surfaces and…
Quotient Quandles and the Fundamental Latin Alexander Quandle
Sam Nelson, Sherilyn Tamagawa
Defined by Joyce and Matveev, the fundamental quandle is a complete invariant of oriented classical knots. We consider invariants of knots defined from quotients of the fundamental…
Lie Ideal Enhancements of Counting Invariants
Gillian Roxanne Grindstaff, Sam Nelson
We define enhancements of the quandle counting invariant for knots and links with a finite labeling quandle Q embedded in the quandle of units of a Lie algebra \mathfrak{a} using L…