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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.07810 |
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| _version_ | 1866910482893373440 |
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| author | Thomas, Robert S. D. |
| author_facet | Thomas, Robert S. D. |
| contents | Perfect colouring of isonemal fabrics by thin and thick striping of warp and weft with more than two colours is examined where the cells with warps and wefts of the same colour do not appear along diagonal lines (not twilly redundancy). In species 33 to 39, all fabrics of specific orders (linear periods) can be perfectly coloured by thin striping with satin redundancy. In fewer species, all fabrics of specific orders can be perfectly coloured by thick striping in two different ways with doubled satin redundancy. The isonemal fabric 6-1-1 can be used as a redundancy configuration. All these colourings allow the coloured weaving of flat tori and -- a few of them -- cubes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07810 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Colouring isonemal fabrics with more than two colours and non-twilly redundancy Thomas, Robert S. D. Combinatorics 52C20, 05B45, 51M20 Perfect colouring of isonemal fabrics by thin and thick striping of warp and weft with more than two colours is examined where the cells with warps and wefts of the same colour do not appear along diagonal lines (not twilly redundancy). In species 33 to 39, all fabrics of specific orders (linear periods) can be perfectly coloured by thin striping with satin redundancy. In fewer species, all fabrics of specific orders can be perfectly coloured by thick striping in two different ways with doubled satin redundancy. The isonemal fabric 6-1-1 can be used as a redundancy configuration. All these colourings allow the coloured weaving of flat tori and -- a few of them -- cubes. |
| title | Colouring isonemal fabrics with more than two colours and non-twilly redundancy |
| topic | Combinatorics 52C20, 05B45, 51M20 |
| url | https://arxiv.org/abs/2406.07810 |