Differences

This shows you the differences between two versions of the page.

--- category_mathematics [2011-01-06 12:55] – 87.210.211.132
+++ category_mathematics [2021-06-11 14:25] – timbo
@@ Line 38: / Line 38: @@
   * "A Computational Introduction to Number Theory and Algebra" > http://shoup.net/ntb/
   * various online textbooks > http://www.math.gatech.edu/%7Ecain/textbooks/onlinebooks.html
+==== 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