# Differences

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table_seating [2021-06-12 12:03] nik |
table_seating [2021-06-17 07:48] (current) timbo |
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- | arranging a group of people into a number of tables so that everyone sits with everyone else. | + | 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. |

- | A strict version is an affine plane. More generally we want a [[https:// | + | * 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 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. | ||

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+ | ===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, | ||

+ | | ||

+ | More generally we want a [[https:// | ||

Strict versions include [[https:// | Strict versions include [[https:// | ||

- | In less strict cases we allow people to meet more often, or not to meet. | + | === 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. | ||

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

The " | The " |