poset
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English
Etymology
Abbreviation of partially ordered set. Coined by American mathematician Garrett Birkhoff in his Lattice Theory.
Pronunciation
- IPA(key): /ˈpəʊsɛt/
Audio (Southern England): (file)
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".
- 1999, Manfred Stern, Semimodular Lattices: Theory and Applications, Cambridge University Press, page 189:
- The combinatorial interest in posets is largely due to two unoriented graphs associated with a given poset: the comparability graph (which we shall not consider here) and the covering graph.
- 1973, Barbara L. Osofsky, Homological Dimensions of Modules, American Mathematical Society, →ISBN, page 76,
Synonyms
- See also Thesaurus:partially ordered set
Derived terms
Related terms
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
Participle
poset
Serbo-Croatian
Alternative forms
Pronunciation
Noun
pȍset m (Cyrillic spelling по̏сет)