Minimal Generating sets of Reidemeister moves
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915636628684800 |
|---|---|
| author | Ito, Noboru Iwamoto, Yuichiro |
| author_facet | Ito, Noboru Iwamoto, Yuichiro |
| contents | 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 include a coherent Reidemeister move of type II. We also classify all minimal generating sets that include a braid-type Reidemeister move of type III. Beyond these two cases, we identify 16 possible candidates for minimal generating sets. Among them, we prove that 12 are indeed minimal, whereas the minimality and even the generating property of the remaining 4 sets remains unsolved (Remark 5.1). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19918 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimal Generating sets of Reidemeister moves Ito, Noboru Iwamoto, Yuichiro Geometric Topology Combinatorics 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 include a coherent Reidemeister move of type II. We also classify all minimal generating sets that include a braid-type Reidemeister move of type III. Beyond these two cases, we identify 16 possible candidates for minimal generating sets. Among them, we prove that 12 are indeed minimal, whereas the minimality and even the generating property of the remaining 4 sets remains unsolved (Remark 5.1). |
| title | Minimal Generating sets of Reidemeister moves |
| topic | Geometric Topology Combinatorics |
| url | https://arxiv.org/abs/2511.19918 |