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
Famous quotes containing the word examples:
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (16881744)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (15331592)
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (18961966)