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Antichain

In mathematics, in the area of order theory, an antichain is a subset of a partially ordered set such that any two distinct elements in the subset are incomparable.

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Overview

Definitions

Height and width

Sperner families

  • OEIS On-Line Encyclopedia of Integer Sequences

Join and meet operations

Computational complexity

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Antichain

Nodes31
Edges30
Triples30
Avg. degree1.94
Density0.064516
Components1

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Antichain

Top relations

related to Definitions · 5
Antichain → An, However, If, Let, Two
related to Height and width · 5
Antichain → Any, Dilworth's, Mirsky's, Similarly, The
related to Join and meet operations · 5
Antichain → Any, Birkhoff's, In, Similarly, The
related to Sperner families · 5
Antichain → An, Dedekind, Even, Sperner, The
related to External links · 4
Antichain → Eric, MathWorld, PlanetMath, Weisstein
is a · 3
Antichain → antichain that has cardinality at least as large as every other antichain, antichain that is not a proper subset of any other antichain, subset of a partially ordered set such that any two distinct elements in the subset are incomparable.The size of the largest antichain in a finite partially ordered set is known…
related to Computational complexity · 3
Antichain → Counting, In, P-complete

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Important terminology

set ordered partially antichains finite displaystyle number elements order two width theorem join meet subset chain equals subsets distributive lattice

Entity relationships Subject–Predicate–Object triples

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SubjectPredicateObjectConfidenceSrc
Antichainis asubset of a partially ordered set such that any two distinct elements in the subset are incomparable.The size of the largest antichain in a finite partially ordered set is known…0.90text
Antichainis aantichain that is not a proper subset of any other antichain0.90text
Antichainis aantichain that has cardinality at least as large as every other antichain0.90text
Antichainrelated to Computational complexityIn0.60section
Antichainrelated to Computational complexityCounting0.60section
Antichainrelated to Computational complexityP-complete0.60section
Antichainrelated to DefinitionsLet0.60section
Antichainrelated to DefinitionsTwo0.60section
Antichainrelated to DefinitionsIf0.60section
Antichainrelated to DefinitionsAn0.60section
Antichainrelated to DefinitionsHowever0.60section
Antichainrelated to External linksWeisstein0.60section

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