poset

See also: pośet and posset

English

Etymology

Abbreviation of partially ordered set.

Pronunciation

• IPA^(key): /ˈpəʊsɛt/

• Audio (Southern England)

  (file)

Noun

poset (plural posets)

1. (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.

Synonyms

• See also Thesaurus:partially ordered set

Derived terms

• algebraic poset

 

Further reading

• Hasse diagram on Wikipedia.Wikipedia
• Lattice (order) on Wikipedia.Wikipedia

Anagrams

• ETOPS, Poets, Potes, T pose, T-pose, Topes, e-stop, estop, pesto, poets, potes, septo-, stoep, stope, topes

Czech

Pronunciation

• IPA^(key): [ˈposɛt]

Participle

poset

1. masculine singular passive participle of posít

Serbo-Croatian

Alternative forms

• pȍsjet (Ijekavian)
• pȍśet (Montenegro)

Pronunciation

• IPA^(key): /pôset/
• Hyphenation: po‧set

Noun

pȍset m (Cyrillic spelling по̏сет)

1. visit

Declension

Declension of poset

	singular	plural
nominative	poset	poseti
genitive	poseta	poseta
dative	posetu	posetima
accusative	poset	posete
vocative	posete	poseti
locative	posetu	posetima
instrumental	posetom	posetima