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| table_seating [2024-04-11 10:19] – [Strict] nik | table_seating [2026-07-11 11:04] (current) – [Upper Version] 88.207.115.163 |
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| Versions include [[https://en.wikipedia.org/wiki/Kirkman%27s_schoolgirl_problem|Kirkman's Schoolgirl Problem]] (15 children walk in groups of 3, can they do this so that all pairs of girls walk together exactly once over a whole week) {[[https://oeis.org/search?q=schoolgirl&sort=&language=german&go=Suche|oeis]]}. This is the question as to resolvable $(v,3,1) $2$-designs, which if I understand it, exist $\iff v = 3 mod 6$. | Versions include [[https://en.wikipedia.org/wiki/Kirkman%27s_schoolgirl_problem|Kirkman's Schoolgirl Problem]] (15 children walk in groups of 3, can they do this so that all pairs of girls walk together exactly once over a whole week) {[[https://oeis.org/search?q=schoolgirl&sort=&language=german&go=Suche|oeis]]}. This is the question as to resolvable $(v,3,1) 2\text{–designs}$, which if I understand it, exist $\iff v = 3 mod 6$. |
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| For pairs, resolvable $(v,2,1) 2$-designs exist only for $even v, v >= 4$. | For pairs, resolvable $(v,2,1) 2\text{–designs}$ exist only for $even v, v >= 4$. |
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| Table size 4: Resolvable (v,k,1)- 2-designs. | Table size 4: Resolvable $(v,k,1) 2\text{–designs}$. |
| [[https://www.semanticscholar.org/paper/The-spectrum-of-resolvable-designs-with-block-size-Vasiga-Furino/364fb4a75a38493ed2c86fa3589adfee6d2714f5|This paper]] says that necessary numerical conditions are sufficient except for a case that need not concern us. | [[https://www.semanticscholar.org/paper/The-spectrum-of-resolvable-designs-with-block-size-Vasiga-Furino/364fb4a75a38493ed2c86fa3589adfee6d2714f5|This paper]] says that necessary numerical conditions are sufficient except for a case that need not concern us. |
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| If we have people sitting at round tables and only interacting with their neighbours, then we have the more difficult [[https://en.wikipedia.org/wiki/Oberwolfach_problem|Oberwolfach Problem]] | If we have people sitting at round tables and only interacting with their neighbours, then we have the more difficult [[https://en.wikipedia.org/wiki/Oberwolfach_problem|Oberwolfach Problem]] |
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| | ==== Discussion ==== |
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| | A summary of the problem and motivations, [[https://loosediary.wordpress.com/2021/12/20/may-i-sit-here/|May I sit here?]] by Tim Boykett |
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