poset

Etymology
Abbreviation of.

Noun

 * 1)  A partially ordered set.
 * 2) * 1973, Barbara L. Osofsky, Homological Dimensions of Modules,, ISBN 0821816624, page 76,
 * 42. Definition. A poset (partially ordered set) (X, ≤) (usually written just X) is a set X together with a transitive, antisymmetric relation ≤ on X.
 * 43. Definition. A linearly ordered set or chain is a poset (X, ≤), such that ∀a, b ∈ X, either a ≤ b or b ≤ a or a = b.
 * 1) * 1998, Yuri A. Drozd, Representations of bisected posets and reflection functors, Idun Reiten, Sverre O. Smalø, Øyvind Solberg (editors), Algebras and Modules II, (for ), page 153,
 * We construct a complete set of reflection functors for the representations of posets and prove that they really have the usual properties. In particular, when the poset is of finite representation type, all of its indecomposable representations can be obtained from some "trivial" ones via relations. To define such reflection functors, a wider class of matrix problem is introduced, called "representations of bisected posets".

Synonyms

 * See also Thesaurus:partially ordered set

Noun

 * 1) visit