2025/12/10 by Isaias Bahena, Bahena, Isaias, Thomas Kindred +3
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Coding theory and cryptography #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2512.09887
openalex publication_date 2025/12/10 · openalex created_date 2025/12/12 · openalex updated_date 2026/07/28
We describe a way of encoding a Kauffman state as a set of tuples, similar to a Gauss code. Then we describe a procedure for using these state codes to determine the unoriented genus and crosscap number of any prime alternating knot or link. Finally, we compute these values for all such links through 14 crossings and all such knots through 19 crossings (this data is new for links with 10-14 crossings and knots with 14-19 crossings), and we identify several intriguing patterns in the resulting data.