2022/05/13 by Kishin Sasaki, Sasaki, Kishin
Computer Science · Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Software Engineering Research
paper · pdf · doi:10.48550/arxiv.2205.06490
openalex publication_date 2022/05/13 · openalex created_date 2023/02/13 · openalex updated_date 2026/07/28
We first prove that, infinitely many pairs of trivial knot diagrams that are transformed into each other by applying Reidemeister moves I and III are NOT transformed into each other by a sequence of the Reidemeister moves I that increase the number of crossings, followed by a sequence of Reidemeister moves III, followed by a sequence of the Reidemeister moves I that decrease the number of crossings. To create a simple sequence between link diagrams that are transformed into each other by applying finitely many Reidemeister moves I and III, we prove that the link diagrams are always transformed into each other by applying an I-generalized ordered sequence.