interval sublattice

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Complete lattice — In mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet). Complete lattices appear in many applications in mathematics and computer science. Being a special instance of… … Wikipedia
Modular lattice — Hasse diagram of N5, the smallest non modular lattice. In the branch of mathematics called order theory, a modular lattice is a lattice that satisfies the following self dual condition: Modular law x ≤ b implies… … Wikipedia
Noncrossing partition — A noncrossing partition of ten points In combinatorial mathematics, the topic of noncrossing partitions has assumed some importance because of (among other things) its application to the theory of free probability. The set of all noncrossing… … Wikipedia

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