2 papers
math.GT2026
Minimal Generating Sets of Singular Reidemeister Moves and Their Classification
Noboru Ito, Yuichiro Iwamoto
Singular knot theory extends classical knot theory by allowing transverse double points without over/under information, together with singular Reidemeister moves of types IV and V.…
math.GT2025
Minimal Generating sets of Reidemeister moves
Noboru Ito, Yuichiro Iwamoto
We determine whether each known generating set of arbitrary oriented Reidemeister moves is minimal. We then provide a complete classification of minimal generating sets that includ…