Algorithmic recognition of quasipositive 4-braids of algebraic length three
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2015
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| _version_ | 1866912142025818112 |
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| author | Orevkov, Stepan Yu. |
| author_facet | Orevkov, Stepan Yu. |
| contents | We give an algorithm to decide whether a given braid with four strings is a product of three factors which are conjugates of standard generators of the braid group. The algorithm is of polynomial time. It is based on the Garside theory. We give also a polynomial algorithm to decide if a given braid with any number of strings is a product of two factors which are conjugates of given powers of the standard generators (in my previous paper this problem was solved without polynomial estimates). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1504_06612 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Algorithmic recognition of quasipositive 4-braids of algebraic length three Orevkov, Stepan Yu. Group Theory 20F36 We give an algorithm to decide whether a given braid with four strings is a product of three factors which are conjugates of standard generators of the braid group. The algorithm is of polynomial time. It is based on the Garside theory. We give also a polynomial algorithm to decide if a given braid with any number of strings is a product of two factors which are conjugates of given powers of the standard generators (in my previous paper this problem was solved without polynomial estimates). |
| title | Algorithmic recognition of quasipositive 4-braids of algebraic length three |
| topic | Group Theory 20F36 |
| url | https://arxiv.org/abs/1504.06612 |