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--- table_seating [2024-04-11 10:20] – [Strict] nik
+++ table_seating [2024-04-11 10:26] – [Strict] nik
@@ Line 15: / Line 15: @@
-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 $\iff v = 3 mod 6$.
-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 $even v, v >= 4$.
-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.