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category_mathematics [2021-06-11 14:25] – timbocategory_mathematics [2021-06-12 12:14] (current) – nik
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   * various online textbooks > http://www.math.gatech.edu/%7Ecain/textbooks/onlinebooks.html   * various online textbooks > http://www.math.gatech.edu/%7Ecain/textbooks/onlinebooks.html
  
 +=== Table Seatings ===
  
- +  * see [[table seating]]
-==== Table Seatings ==== +
- +
-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 +
- +
  

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