# Differences

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

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table_seating [2021-12-08 08:44] timbo |
table_seating [2022-04-04 03:32] (current) nik |
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==== Table Seatings ==== | ==== Table Seatings ==== | ||

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The general problem is arranging a group of people into a number of tables so that everyone sits with everyone else. There are multiple versions for this. | The general problem is arranging a group of people into a number of tables so that everyone sits with everyone else. There are multiple versions for this. | ||

- | * The strict version is that all tables are the same size and that after the required number of rounds, everyone has shared a table with every other person exactly once | + | * The **strict** version is that all tables are the same size and that after the required number of rounds, everyone has shared a table with every other person exactly once |

- | * The lower version requires that each person shares a table with each other person at most once | + | * The **lower version** requires that each person shares a table with each other person at most once |

- | * The upper version requires that each person shares a table with each other person at least once | + | * The **upper version** requires that each person shares a table with each other person at least once |

Some general thoughts. Each sitting defines a partition of the set of people, each part is one table. | Some general thoughts. Each sitting defines a partition of the set of people, each part is one table. | ||

- | ===Strict=== | + | ====Strict==== |

A strict version is an affine plane. Example 25 people in 5 tables of 5, Point set is Z_5 x Z_5,we take the tables to be the lines L(a, | A strict version is an affine plane. Example 25 people in 5 tables of 5, Point set is Z_5 x Z_5,we take the tables to be the lines L(a, | ||

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[[https:// | [[https:// | ||

- | | + | ==== Lower Version==== |

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- | === Lower Version=== | + | |

Just leave out some sittings on a strict version. Perhaps add a few nonexistant people to get a better distribution of people on tables with not all tables always full. | Just leave out some sittings on a strict version. Perhaps add a few nonexistant people to get a better distribution of people on tables with not all tables always full. | ||

- | === Upper Version === | + | ==== Upper Version ==== |

The " | The " |