Boyd-Maxwell ball packings
In the recent study of infinite root systems, fractal patterns of ball packings were observed while visualizing roots in affine space. In fact, the observed fractals are exactly the ball packings described by Boyd and Maxwell. This correspondence is a corollary of a more fundamental result: given a...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2014-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/2384/pdf |
| _version_ | 1797270313021472768 |
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| author | Hao Chen Jean-Philippe Labbé |
| author_facet | Hao Chen Jean-Philippe Labbé |
| author_sort | Hao Chen |
| collection | DOAJ |
| description | In the recent study of infinite root systems, fractal patterns of ball packings were observed while visualizing roots in affine space. In fact, the observed fractals are exactly the ball packings described by Boyd and Maxwell. This correspondence is a corollary of a more fundamental result: given a geometric representation of a Coxeter group in Lorentz space, the set of limit directions of weights equals the set of limit roots. |
| first_indexed | 2024-04-25T02:02:17Z |
| format | Article |
| id | doaj.art-d78e3c6c1e8c4188acfa84afcb4b4e8d |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:02:17Z |
| publishDate | 2014-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-d78e3c6c1e8c4188acfa84afcb4b4e8d2024-03-07T14:53:19ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502014-01-01DMTCS Proceedings vol. AT,...Proceedings10.46298/dmtcs.23842384Boyd-Maxwell ball packingsHao Chen0Jean-Philippe Labbé1Institute of Mathematics [Berlin]Institute of Mathematics [Berlin]In the recent study of infinite root systems, fractal patterns of ball packings were observed while visualizing roots in affine space. In fact, the observed fractals are exactly the ball packings described by Boyd and Maxwell. This correspondence is a corollary of a more fundamental result: given a geometric representation of a Coxeter group in Lorentz space, the set of limit directions of weights equals the set of limit roots.https://dmtcs.episciences.org/2384/pdfsphere packingball packinginfinite coxeter groupsinfinite root systemslimit rootscoxeter graphs[info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-co] mathematics [math]/combinatorics [math.co] |
| spellingShingle | Hao Chen Jean-Philippe Labbé Boyd-Maxwell ball packings Discrete Mathematics & Theoretical Computer Science sphere packing ball packing infinite coxeter groups infinite root systems limit roots coxeter graphs [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] |
| title | Boyd-Maxwell ball packings |
| title_full | Boyd-Maxwell ball packings |
| title_fullStr | Boyd-Maxwell ball packings |
| title_full_unstemmed | Boyd-Maxwell ball packings |
| title_short | Boyd-Maxwell ball packings |
| title_sort | boyd maxwell ball packings |
| topic | sphere packing ball packing infinite coxeter groups infinite root systems limit roots coxeter graphs [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/2384/pdf |
| work_keys_str_mv | AT haochen boydmaxwellballpackings AT jeanphilippelabbe boydmaxwellballpackings |