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Linear extension

In order theory, a branch of mathematics, a linear extension of a partial order is a total order (or linear order) that is compatible with the partial order. As a classic example, the lexicographic order of totally ordered sets is a linear extension of their product order.

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Overview

Definitions

Order-extension principle

Related results

Algebraic combinatorics

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Linear extension

Nodes47
Edges46
Triples13
Avg. degree1.96
Density0.042553
Components1

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Linear extension

Top relations

related to Algebraic combinatorics · 5
Linear extension → Counting, For, Similarly, This, Young
related to Related results · 5
Linear extension → Among, Despite, P-complete, Several, The
related to Linear extension of a preorder · 2
Linear extension → Here, The
related to Linear extension of a partial order · 1
Linear extension → Given

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Important terminology

linear order displaystyle partial extension extensions principle preorder set precsim ordered every total order-extension finite condition elements number orders equivalent

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Linear extensionrelated to Algebraic combinatoricsCounting0.60section
Linear extensionrelated to Algebraic combinatoricsThis0.60section
Linear extensionrelated to Algebraic combinatoricsYoung0.60section
Linear extensionrelated to Algebraic combinatoricsSimilarly0.60section
Linear extensionrelated to Algebraic combinatoricsFor0.60section
Linear extensionrelated to Linear extension of a partial orderGiven0.60section
Linear extensionrelated to Linear extension of a preorderThe0.60section
Linear extensionrelated to Linear extension of a preorderHere0.60section
Linear extensionrelated to Related resultsThe0.60section
Linear extensionrelated to Related resultsSeveral0.60section
Linear extensionrelated to Related resultsDespite0.60section
Linear extensionrelated to Related resultsP-complete0.60section

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