Vries, Rick de (2025) Building a Table of Knots. Master's Thesis / Essay, Mathematics.
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Abstract
In this thesis, the goal is to produce a table of knots of up to 10 crossings. To achieve this, we first cover basic knot theory which defines equivalence of knots, various moves that can be applied to knots, properties knots can have and representing knots numerically. After this, we cover knot invariants like the crossing number, the Jones polynomial and the Theta invariant. Then we introduce plantri, a graph generating tool that will be used to generate our starting dataset. Using all these tools, we will build a knot table using a computer in Python. In the end, our final result is an almost perfect knot table. For knots with up to nine crossings (inclusive), our results match the number of distinct knots listed in other tables, such as KnotInfo. For ten crossings, our results almost match. We find four extra knots, which, after comparison with KnotInfo, are determined to be reducible.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Veen, R.I. van der and Martynchuk, N. |
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 07 Aug 2025 06:50 |
| Last Modified: | 07 Aug 2025 06:50 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/36707 |
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