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math.GT2024
Thistlethwaite Theorems for Knotoids and Linkoids
Sergei Chmutov, Qingying Deng, Joanna A. Ellis-Monaghan +2
The classical Thistlethwaite theorem for links can be phrased as asserting that the Kauffman bracket of a link can be obtained from an evaluation of the Bollobás-Riordan polynomia…
math.GT2024
Planar Equivalence of Knotoids and Quandle Invariants
Mohamed Elhamdadi, Wout Moltmaker, Masahico Saito
While knotoids on the sphere are well-understood by a variety of invariants, knotoids on the plane have proven more subtle to classify due to their multitude over knotoids on the s…
math.GT2024
The Mock Alexander Polynomial for Knotoids and Linkoids
Joanna A. Ellis-Monaghan, Neslihan Gügümcü, Louis H. Kauffman +1
The mock Alexander polynomial is an extension of the classical Alexander polynomial, defined and studied for (virtual) knots and knotoids by the second and third authors. In this p…