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| table_seating [2024-04-11 10:22] – [Strict] nik | table_seating [2024-04-11 10:26] (current) – [Strict] nik |
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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 $(v,3,1) 2\text{--designs}$, 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 $(v,2,1) 2\text{--designs}$ 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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