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Kyungpook Mathematical Journal 2024; 64(4): 549-557

Published online December 31, 2024 https://doi.org/10.5666/KMJ.2024.64.4.549

Copyright © Kyungpook Mathematical Journal.

On Two Kinds of Clasp-Pass Moves for Knots

Hideo Takioka

School of Mechanical Engineering, College of Science and Engineering, Kanazawa University, Kakuma-Machi, Kanazawa, 920-1192, Japan
e-mail: takioka@se.kanazawa-u.ac.jp

Received: July 15, 2022; Revised: September 21, 2022; Accepted: October 11, 2022

Abstract

We introduce two kinds of clasp-pass moves for knots called self, nonself-clasppass moves (SCP, NCP-moves) related to self, nonself-crossings. Moreover, we introduce another two kinds of clasp-pass moves for knots called clasp-pass moves of types II, X (CPII, CPX-moves) related to clasp disks. In this paper, we show that knots K and K′ are related by a single SCP-move (resp. NCP-move) if and only if K and K′ are related by a single CPII-move (resp. CPX-move).

Keywords: Clasp-pass move, &Gamma,-polynomial