Knot Mosaics with Corner Connection Tiles
Fuente:
arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866913294307033088 |
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| author | Heap, Aaron Donovan, Una Grossman, Riley Laine, Nickolas McDermott, Connor Paone, Marcus Southcott, Drew |
| author_facet | Heap, Aaron Donovan, Una Grossman, Riley Laine, Nickolas McDermott, Connor Paone, Marcus Southcott, Drew |
| contents | A knot mosaic is a representation of a knot or link on a square grid using a collection of tiles that are either blank or contain a portion of the knot diagram. Traditionally, a piece of the knot on one tile connects to a piece of the knot on an adjacent tile at a connection point that is located at the midpoint of a tile edge. We introduce a new set of tiles in which the connection points are located at corners of the tile. By doing this, we can create more efficient knot mosaics for knots with small crossing number. In particular, when using these corner connection tiles, it is possible to create knot mosaic diagrams for all knots with crossing number 8 or less on a mosaic that is no larger and uses fewer non-blank tiles than is possible using the traditional tiles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_09276 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Knot Mosaics with Corner Connection Tiles Heap, Aaron Donovan, Una Grossman, Riley Laine, Nickolas McDermott, Connor Paone, Marcus Southcott, Drew Geometric Topology 57K10 A knot mosaic is a representation of a knot or link on a square grid using a collection of tiles that are either blank or contain a portion of the knot diagram. Traditionally, a piece of the knot on one tile connects to a piece of the knot on an adjacent tile at a connection point that is located at the midpoint of a tile edge. We introduce a new set of tiles in which the connection points are located at corners of the tile. By doing this, we can create more efficient knot mosaics for knots with small crossing number. In particular, when using these corner connection tiles, it is possible to create knot mosaic diagrams for all knots with crossing number 8 or less on a mosaic that is no larger and uses fewer non-blank tiles than is possible using the traditional tiles. |
| title | Knot Mosaics with Corner Connection Tiles |
| topic | Geometric Topology 57K10 |
| url | https://arxiv.org/abs/2306.09276 |