2023/01/06 by Rhea Palak Bakshi, Bakshi, Rhea Palak, Huizheng Guo +7
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Biochemical and Structural Characterization #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Primary: 57K10 Secondary: 57M12 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2301.02645
openalex publication_date 2023/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a reduced alternating diagram of a knot with a prime determinant p, the Kauffman-Harary conjecture states that every non-trivial Fox p-coloring of the knot assigns different colors to its arcs. In this paper, we prove a generalization of the conjecture stated nineteen years ago by Asaeda, Przytycki, and Sikora: for every pair of distinct arcs in the reduced alternating diagram of a prime link with determinant δ, there exists a Fox δ-coloring that distinguishes them.