From en.wiktionary.org:
[pośet]
** English
[Partially ordered set]
*** Etymology
Abbreviation of [en]. [en] in his _Lattice Theory_.
*** Pronunciation
- [en]
- [en]
*** Noun
[en-noun]
1. [en] A partially ordered set .
2. * 1973, Barbara L. Osofsky, _Homological Dimensions of Modules_ , [American Mathematical Society] , [0821816624] , page 76,
3. *: 42. _Definition._ A POSET (partially ordered set) ( _X_ , ≤) (usually written just _X_ ) is a set _X_ together with a transitive, antisymmetric relation ≤ on _X_ .
4. *: 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_ .
5. * 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 (see https://books.google.com.au/books?id=vcQvsh6FKPoC&pg=PA153&dq=%22poset%22%7C%22posets%22&hl=en&sa=X&ved=0ahUKEwi9sN7lr-LbAhUDiLwKHZMuDVcQ6AEI3wEwIg#v=onepage&q=%22poset%22%7C%22posets%22&f=false) ,
6. *: 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 ".
7. * {{ quote-book | en | year=1999 | author=Manfred Stern | title=Semimodular Lattices: Theory and Applications | pageurl=https://books.google.com.au/books?id=VVYd2sC19ogC&pg=PA189&dq=%22poset%22%7C%22posets%22&hl=en&sa=X&ved=0ahUKEwi9sN7lr-LbAhUDiLwKHZMuDVcQ6AEIwwEwHQ#v=onepage&q=%22poset%22%7C%22posets%22&f=false | page=189 | publisher=w:Cambridge University Press
|passage=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
[en]
**** Related terms
- [en]
*** Further reading
- [Hasse diagram]
- [Lattice (order)]
*** Anagrams
- [en]
** Czech
*** Pronunciation
- [cs-IPA]
*** Participle
[cs]
1. [cs]
** Serbo-Croatian
*** Alternative forms
- [sh]
- [sh]
*** Pronunciation
- [sh]
- [sh]
*** Noun
[pȍset]
1. visit
**** Declension
{{sh-decl-noun |poset|poseti |poseta|poseta |posetu|posetima |poset|posete
|posete|poseti |posetu|posetima |posetom|posetima }}