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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]] | see [[table seating]] | ||
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- | arranging a group into a number of tables so that everyone sits with everyone else. | ||
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- | 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. | ||
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- | Strict versions include Kirkman' | ||
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- | In other cases we need to either allow people not to meet, or to meet more often. | ||
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- | The Dagstuhl Happy Diner problem is the version where everyone meets at least once. | ||
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- | Equitable Resolvable coverings seem also to be a more strict form, where we try to allow people to meet at most twice. | ||
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- | If we have people sitting at round tables and only interacting with their neighbours, then we have the Oberwolfach Problem: | ||
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