Differences

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--- table_seating [2022-04-04 03:32] – nik
+++ table_seating [2024-04-11 10:09] – [Strict] nik
@@ Line 10: / Line 10: @@
 ====Strict====
-A strict version is an affine plane. Example 25 people in 5 tables of 5, Point set is Z_5 x Z_5,we take the tables to be the lines L(a,b)={(x,y)| y=ax+b} and L(a)={(a,y)| y in Z_5}, the sitting is a parallel class (the 5 lines with the same slope a), so we have 6 sittings, L(a,b) for a=0,1,2,3,4 and then the parallel class of L(a).
+A strict version is an affine plane. Example 25 people in 5 tables of 5, Point set is $Z_5 x Z_5$, we take the tables to be the lines L(a,b)={(x,y)| y=ax+b} and L(a)={(a,y)| y in Z_5}, the sitting is a parallel class (the 5 lines with the same slope a), so we have 6 sittings, L(a,b) for a=0,1,2,3,4 and then the parallel class of L(a).
 More generally we want a [[https://en.wikipedia.org/wiki/Block_design#Resolvable_2-designs|resolvable 2-design]]. We want resolvable (v,k,1) designs. Resolvable is the parallelism. Maybe there is something like discrete hyperbolic geometry to deal with this, but we seem to have better combinatorial ideas below.