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Polymatroid: Definition, Relation to generalized permutahedra & Discrete polymatroids

In mathematics, a polymatroid is a polytope associated with a submodular function. The notion was introduced by Jack Edmonds in 1970. It is also a generalization of the notion of a matroid.

Language: English [EN]
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Polymatroid topic overview

The analysis highlights Definition, Relation to generalized permutahedra and Discrete polymatroids as prominent areas in the source structure around Polymatroid.

Related topics
21
Source areas
6
Connected nodes
27
Extracted relationships
26
Concept neighborhoods
14
Bridge connections
27

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Definition · 7 topics
Relation to generalized permutahedra · 5 topics
Overview · 4 topics
Contrapolymatroids · 2 topics
Discrete polymatroids · 2 topics
Properties · 1 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Definition

Discrete polymatroids

Relation to generalized permutahedra

Properties

Contrapolymatroids

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Polymatroid connects Entity context

The extracted context around Polymatroid shows recurring relationship patterns in the source. For example, Polymatroid → If, In, Let, That, Then, This, Under, We, While Another extracted example is Polymatroid → matroid, pair, polymatroid for which the codomain of f, polytope associated with a submodular function. Use these groups to spot repeated connection types before inspecting the individual relationships.

Polymatroid

Top relations

related to Matroidal definition · 9
Polymatroid → If, In, Let, That, Then, This, Under, We, While
is a · 4
Polymatroid → matroid, pair, polymatroid for which the codomain of f, polytope associated with a submodular function
related to Discrete polymatroids · 4
Polymatroid → Also, Discrete, Given, Thus
related to Polyhedral definition · 3
Polymatroid → Let, We, When
related to Contrapolymatroids · 2
Polymatroid → For, This
related to Properties · 2
Polymatroid → EP, Given
related to Vector definition · 2
Polymatroid → If, Let

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

displaystyle set matroid geq function mathbb polytope submodular definition discrete generalized leq textbf polymatroids subseteq integer independent notion permutahedron vector

Polymatroid relationships Subject–Predicate–Object triples

TTTA extracted 26 structured relationships around Polymatroid. Examples in this analysis include Polymatroid → is a → polytope associated with a submodular function and Polymatroid → is a → pair. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Polymatroidis apolytope associated with a submodular function0.90text
Polymatroidis apair0.90text
Polymatroidis apolymatroid for which the codomain of f0.90text
Polymatroidis amatroid0.90text
Polymatroidrelated to ContrapolymatroidsFor0.60section
Polymatroidrelated to ContrapolymatroidsThis0.60section
Polymatroidrelated to Discrete polymatroidsDiscrete0.60section
Polymatroidrelated to Discrete polymatroidsGiven0.60section
Polymatroidrelated to Discrete polymatroidsThus0.60section
Polymatroidrelated to Discrete polymatroidsAlso0.60section
Polymatroidrelated to Matroidal definitionIn0.60section
Polymatroidrelated to Matroidal definitionThat0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Polymatroid bring nearby vocabulary together. In this analysis, examples include Displaystyle, Integer and Function. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Polymatroid
    • Displaystyle
    • Integer
    • Function
    • Geq
    • Discrete
    • Definition
    • Mathbb
    • Matroid
    • Polytope
    • Submodular
    • Set
    • Associated
  • polymatroid
    • Displaystyle
    • Integer
    • Function
    • Geq
    • Discrete
    • Definition
    • Mathbb
    • Matroid
    • Polytope
    • Submodular
    • Set
    • Associated
  • submodular function
    • Submodular
    • Set
    • Definition
    • Mathbb
    • Geq
    • Polymatroid
    • Displaystyle
    • Subseteq
    • Non-decreasing
    • Rightarrow
    • Defined
    • Finite
  • definition
    • Function
    • Leq
    • Matroidal
    • Defined
    • Set
    • Vector
    • Matroid
    • Integer
    • Polymatroid
    • Polymatroids
    • Discrete
    • Displaystyle
  • finite set
    • Non-decreasing
    • Rightarrow
    • Set
    • Submodular
    • Matroidal
    • Defined
    • Vector
    • Vectors
    • Function
    • Independent
    • Mathbb
    • Permutahedra
  • discrete polymatroids
    • Polymatroids
    • Matroidal
    • Subseteq
    • Polymatroid
    • Geq
    • Leq
    • Non-decreasing
    • Rightarrow
    • Set
    • Displaystyle
    • Defined
    • Permutahedra
  • relation to generalized permutahedra
    • Permutahedra
    • Permutahedron
    • Thus
    • Mathbb
    • Non-decreasing
    • Rightarrow
    • Subseteq
    • Polytope
    • Submodular
    • Vector
    • Polymatroids
    • Geq
  • matroid
    • Definition
    • Polymatroid
    • Rank
    • Integer
    • Displaystyle
    • Notion
    • Defined
    • Permutahedra
    • Thus
    • Independent
    • Polymatroids
    • Subseteq

Connections between topic areas Semantic bridges

For Polymatroid, one of the stronger structural bridges in this analysis connects Polymatroid with Definition. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
PolymatroidDefinition · splits 20 ⟂ 8
PolymatroidRelation to generalized permutahedra · splits 22 ⟂ 6
PolymatroidOverview · splits 23 ⟂ 5
PolymatroidDiscrete polymatroids · splits 25 ⟂ 3
PolymatroidContrapolymatroids · splits 25 ⟂ 3

Map overview Semantic statistics

Polymatroid

Nodes28
Edges27
Triples26
Avg. degree1.93
Density0.071429
Components1

Source & methodology

TTTA analyzes the structure around Polymatroid to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Definition, Relation to generalized permutahedra & Discrete polymatroids, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Polymatroid · EN edition · Analysis: TopicsToTalkAbout

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