2020/07/09 by Christopher R. Cornwell, Cornwell, Christopher R., Nathan McNew +1
Mathematics · Social Sciences · #05A #57K #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Names, Identity, and Discrimination Research
paper · pdf · doi:10.48550/arxiv.2007.04917
openalex publication_date 2020/07/09 · openalex created_date 2022/09/09 · openalex updated_date 2026/07/28
Noting that cycle diagrams of permutations visually resemble grid diagrams used to depict knots and links in topology, we consider the knot (or link) obtained from the cycle diagram of a permutation. We show that the permutations which correspond in this way to an unknot are enumerated by the Schröder numbers, and also enumerate the permutations corresponding to an unlink. The proof uses Bennequin's inequality.