Dictionary

antichain en · NOUN

Etymology

Etymology tree Proto-Indo-European *h₂ent- Proto-Indo-European *-s Proto-Indo-European *h₂énts Proto-Indo-European *-i Proto-Indo-European *h₂énti Ancient Greek ᾰ̓ντῐ́ (ăntĭ́) Ancient Greek ἀντι- (anti-)der. English anti- Proto-Italic *katesnā Latin catēna Old French chaeinebor. Middle English cheyne English chain English antichain From anti- + chain.

Meanings

1. (error-lua-exec) A subset, A, of a partially ordered set, (P, ≤), such that no two elements of A are comparable with respect to ≤.
   • 2013, Vijay K. Garg, Maximal Antichain Lattice Algorithms for Distributed Computations, Proceedings, Davide Frey, Michel Raynal, Saswati Sarkar, Rudrapatna K. Shyamasundar, Prasun Sinha (editors), Distributed Computing and Networking: 14th International Conference, ICDCN, Springer, LNCS 7730, page 245, We first define three different but isomorphic lattices: the lattice of maximal antichain ideals, the lattice of maximal antichains and the lattice of strict ideals.
   • First of all, Zorn's Lemma implies that every uncountable antichain in T is contained in a maximal uncountable antichain. So it suffices to make sure that T has no maximal uncountable antichains. 1997, Winfried Just, Martin Weese, Discovering Modern Set Theory II: Set-Theoretic Tools for Every Mathematician, American Mathematical Society, page 140:

Forms

Deriveds

maximal antichain

Translations (3)

fi antiketju (subset of a partially ordered set) · es anticadena (subset of a partially ordered set) · it anticatena (subset of a partially ordered set)