2024/08/21 by Stefan Friedl, Friedl, Stefan, Filip Misev +3
Computer Science · Mathematics · #57K10 #Algorithms and Data Compression #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2408.11618
openalex publication_date 2024/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The ribbon number r(K) of a ribbon knot K ⊂ S3 is the minimal number of ribbon intersections contained in any ribbon disk bounded by K. We find new lower bounds for r(K) using det(K) and ΔK(t), and we prove that the set \mathfrakRr~=~\ΔK(t)~:~r(K)~≤~r\ is finite and computable. We determine \mathfrakR2 and \mathfrakR3, applying our results to compute the ribbon numbers for all ribbon knots with 11 or fewer crossings, with three exceptions. Finally, we find lower bounds for ribbon numbers of links derived from their Jones polynomials.