EnglishWikipedia has an article on:

Partially ordered set

Wikipedia

Abbreviation ofpartially ordered set.Coined by American mathematicianGarrett Birkhoff in hisLattice Theory.

• IPA^(key): /ˈpəʊsɛt/

• Audio(Southern England):

  (file)

poset (pluralposets)

1. (set theory, order theory) Apartially ordered set.
   • 1973, Barbara L. Osofsky,Homological Dimensions of Modules,American Mathematical Society,→ISBN, page 76,

     42.Definition. Aposet (partially ordered set) (X, ≤) (usually written justX) is a setX together with a transitive, antisymmetric relation ≤ onX.

     43.Definition. A linearly ordered set or chain is aposet (X, ≤), such that ∀a,b ∈X, eithera ≤b orb ≤a ora =b.

   • 1998, Yuri A. Drozd,Representations of bisectedposets and reflection functors, Idun Reiten, Sverre O. Smalø, Øyvind Solberg (editors),Algebras and Modules II,American Mathematical Society (forCanadian Mathematical Society),page 153,

     We construct a complete set of reflection functors for the representations ofposets and prove that they really have the usual properties. In particular, when theposet 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 bisectedposets".

   • 1999, Manfred Stern,Semimodular Lattices: Theory and Applications,Cambridge University Press,page189:

     The combinatorial interest inposets is largely due to two unoriented graphs associated with a givenposet: the comparability graph (which we shall not consider here) and the covering graph.

• See alsoThesaurus:partially ordered set

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

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

• IPA^(key): [ˈposɛt]

poset

1. masculinesingularpassiveparticiple ofposít

• pȍsjet(Ijekavian)
• pȍśet(Montenegro)

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

pȍset m (Cyrillic spellingпо̏сет)

1. visit

• English terms coined by Garrett Birkhoff
• English coinages
• English 2-syllable words
• English terms with IPA pronunciation
• English terms with audio pronunciation
• English lemmas
• English nouns
• English countable nouns
• en:Set theory
• English terms with quotations
• Czech terms with IPA pronunciation
• Czech non-lemma forms
• Czech past passive participles
• Serbo-Croatian terms with IPA pronunciation
• Serbo-Croatian lemmas
• Serbo-Croatian nouns
• Serbo-Croatian masculine nouns

• Pages with entries
• Pages with 3 entries