2024/11/09 by O'Bryan Cárdenas-Andaur, Cárdenas-Andaur, O'Bryan · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #57K10 #57K12 #57K14 #Algorithms and Data Compression #Cellular Automata and Applications #DNA and Biological Computing #FOS: Mathematics #Geometric Topology (math.GT)
paper · pdf · doi:10.48550/arxiv.2411.06259
openalex publication_date 2024/11/09 · openalex created_date 2024/11/15 · openalex updated_date 2026/07/28
Given a tied link L, the invariant ⟨⟨⋅⟩⟩ generalizes the Kauffman bracket of classical links. However, the analogues of Kauffman states and their relationship to this invariant are not immediately clear. We address this question by defining the Aicardi-Juyumaya states, and show that the contribution of each AJ-state to ⟨⟨⋅⟩⟩ does not depend on the chosen resolution tree. We also present an algorithm to compute the double bracket of a tied link diagram, and use it to find pairs of examples of (oriented) tied links sharing the same Homflypt polynomial but different tied Jones polynomial.