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--- category_mathematics [2021-06-12 11:52] – [Table Seatings] nik
+++ category_mathematics [2021-06-12 12:13] – nik
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 see [[table seating]]
-arranging a group into a number of tables so that everyone sits with everyone else.
-A strict version is an affine plane.
-More generally we want a resolvable 2-design. Resovable is the parallelism. Maybe there is something like discrete hyperbolic geometry to deal with this, but we seem to have better combinatorial ideas below.
-https://en.wikipedia.org/wiki/Block_design#Resolvable_2-designs
-Strict versions include Kirkman's Schoolgitl 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://en.wikipedia.org/wiki/Kirkman%27s_schoolgirl_problem
-https://oeis.org/search?q=schoolgirl&sort=&language=german&go=Suche
-In other cases we need to either allow people not to meet, or to meet more often.
-The Dagstuhl Happy Diner problem is the version where everyone meets at least once.
-https://github.com/fpvandoorn/Dagstuhl-tables
-https://oeis.org/A318240
-Equitable Resolvable coverings seem also  to be a more strict form, where we try to allow people to meet at most twice.
-https://www.researchgate.net/publication/227715273_Equitable_resolvable_coverings
-https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.10024?saml_referrer
-If we have people sitting at round tables and only interacting with their neighbours, then we have the Oberwolfach Problem:
-https://en.wikipedia.org/wiki/Oberwolfach_problem