30 citations · 184 across the 89 of their papers we have counts for
6 papers · 1 filter
Biracks and Switch Braid Quivers
Max Chao-Haft, Sam Nelson
We consider birack and switch colorings of braids. We define a switch structure on the set of permutation representations of the braid group and consider when such a representation…
Biquandle Bracket Quivers
Pia Cosma Falkenburg, Sam Nelson
Biquandle brackets define invariants of classical and virtual knots and links using skein invariants of biquandle-colored knots and links. Biquandle coloring quivers categorify the…
Psyquandle Coloring Quivers
Jose Ceniceros, Anthony Christiana, Sam Nelson
We enhance the psyquandle counting invariant for singular knots and pseudoknots using quivers analogously to quandle coloring quivers. This enables us to extend the in-degree polyn…
Skew Brace Enhancements
Melody Chang, Sam Nelson
We use the structure of skew braces to enhance the biquandle counting invariant for virtual knots and links for finite biquandles defined from skew braces. We introduce two new inv…
Tribracket Polynomials
Sam Nelson, Fletcher Nickerson
We introduce a six-variable polynomial invariant of Niebrzydowski tribrackets analogous to quandle,rack and biquandle polynomials. Using the subtribrackets of a tribracket, we addi…
G-Family Polynomials
Sam Nelson, Madeline Brown
We introduce two notions of quandle polynomials for G-families of quandles: the quandle polynomial of the associated quandle and a G-family polynomial with coefficients in the grou…