Order, lattices, ordered algebraic structures Chains, antichains, dimension Concept
Linear extension
Summary
A linear extension of a partial order is a total order on the same set that keeps every relation of the partial order. Every partial order has one, and the order is recovered as the intersection of all of them. Linear extensions are the basis of order dimension, of sorting problems, and of many counting questions about finite posets.
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| Tag | W8DZ5KGGHN |
|---|---|
| URI | m2://W8DZ5KGGHN |
| Kind | concept |
| Writing | W0 stub |
| MSC | 06A05, 06A07 |
| Same as |
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Used by
- XYZ inequality
- Fence
- Order polytope
- Order dimension
- 1/3–2/3 conjecture
- Szpilrajn extension theorem
- Crown
- Order polynomial