Examples
- In a finite linearly ordered set 1,… n, i + 1 covers i for all i between 1 and n − 1 (and there are no other covering relations).
- In the Boolean algebra of the power set of a set S, a subset B of S covers a subset A of S if and only if B is obtained from A by adding one element not in A.
- In Young's lattice, formed by the partitions of all nonnegative integers, a partition λ covers a partition μ if and only if the Young diagram of λ is obtained from the Young diagram of μ by adding an extra cell.
- The Hasse diagram depicting the covering relation of a Tamari lattice is the skeleton of an associahedron.
- The covering relation of any distributive lattice forms a median graph.
- On the real numbers with the usual total order ≤, the cover set is empty: no number covers another.
Read more about this topic: Covering Relation
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