Show pageOld revisionsBacklinksBack to top You've loaded an old revision of the document! If you save it, you will create a new version with this data. Media Files==== Table Seatings ==== arranging a group of people into a number of tables so that everyone sits with everyone else. A strict version is an affine plane. More generally we want a [[https://en.wikipedia.org/wiki/Block_design#Resolvable_2-designs|resolvable 2-design]]. 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. Strict 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]]} In less strict cases we allow people to meet more often, or not to meet. The "[[https://github.com/fpvandoorn/Dagstuhl-tables|Dagstuhl Happy Diner problem]]" is the version where everyone meets at least once. {[[https://oeis.org/A318240|oeis]]} [[https://www.researchgate.net/publication/227715273_Equitable_resolvable_coverings|Equitable Resolvable coverings]] also seem to be a more strict form, where we can allow people to meet at most twice. {[[https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.10024|ref]]} If we have people sitting at round tables and only interacting with their neighbours, then we have the more difficult [[https://en.wikipedia.org/wiki/Oberwolfach_problem|Oberwolfach Problem]] ---- part of [[category mathematics]] Please fill all the letters into the box to prove you're human. Please keep this field empty: SavePreviewCancel Edit summary Note: By editing this page you agree to license your content under the following license: CC Attribution-Share Alike 4.0 International table_seating.1623499381.txt.gz Last modified: 2021-06-12 12:03by nik