poset

== English == === Etymology === Abbreviation of partially ordered set. Coined by American mathematician Garrett Birkhoff in his Lattice Theory. === Pronunciation === IPA(key): /ˈpəʊsɛt/ === Noun === poset (plural posets) (set theory, order theory) A partially ordered set. 1973, Barbara L. Osofsky, Homological Dimensions of Modules, American Mathematical Society, →ISBN, 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. 1998, Yuri A. Drozd, Representations of bisected posets and reflection functors, Idun Reiten, Sverre O. Smalø, Øyvind Solberg (editors), Algebras and Modules II, American Mathematical Society (for Canadian Mathematical Society), 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 ==== Derived terms ==== ==== Related terms ==== causet === Further reading === Hasse diagram on Wikipedia.Wikipedia Lattice (order) on Wikipedia.Wikipedia === Anagrams === stope, potes, Topes, topes, pesto, estop, Petos, T pose, stoep, septo-, Poets, T-pose, e-stop, ETOPS, Potes, poets == Czech == === Pronunciation === IPA(key): [ˈposɛt] === Participle === poset masculine singular passive participle of posít == Serbo-Croatian == === Alternative forms === pȍsjet (Ijekavian) pȍśet (Montenegro) === Pronunciation === IPA(key): /pôset/ Hyphenation: po‧set === Noun === pȍset m inan (Cyrillic spelling по̏сет) visit ==== Declension ====