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Numerical semigroup

In mathematics, a numerical semigroup is a special kind of a semigroup. Its underlying set is the set of all nonnegative integers except a finite number of integers, and the binary operation is the operation of addition of integers. Also, the integer 0 must be an element of the semigroup. For example, while the set {0, 2, 3, 4, 5, 6, ...} is a numerical…

Definition and examples, Embedding dimension, multiplicity & Computation of Frobenius number

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Definition and examples

GcdWell-temperedHarmonic
3 related topics

Embedding dimension, multiplicity

CardinalityEmbedding dimension
2 related topics

Computation of Frobenius number

Worst-case complexityContinued fraction
2 related topics

Overview

SemigroupSetIntegersFiniteBinary operation
11 related topics

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Overview

Definition and examples

Embedding dimension, multiplicity

Frobenius number and genus

Computation of Frobenius number

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Map overview Semantic statistics

Numerical semigroup

Nodes25
Edges24
Triples39
Avg. degree1.92
Density0.08
Components1

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Numerical semigroup

Top relations

related to Apéry Set · 7
Numerical semigroup → Ap, Apéry, Equivalently, Let, The Apéry, The Frobenius, Typically
related to Rödseth's algorithm · 6
Numerical semigroup → Frobenius, Greenberg's, Its, Let, Rödseth's, The
related to Examples · 4
Numerical semigroup → Let, The, Then, Well-tempered
related to Numerical semigroups with embedding dimension three · 4
Numerical semigroup → Every, Frobenius, No, There
related to Special classes of numerical semigroups · 4
Numerical semigroup → An, Frobenius, Such, We
is a · 3
Numerical semigroup → minimal system of generators if none of its proper subsets generates the numerical semigroup, numerical semigroup such that it cannot be written as the intersection of two numerical semigroups properly containing it, special kind of a semigroup
related to Definition · 3
Numerical semigroup → If, Let, SN
related to Frobenius number and genus · 3
Numerical semigroup → Frobenius, The, There
related to Theorem · 3
Numerical semigroup → Let, Moreover, Then
related to Embedding dimension, multiplicity · 2
Numerical semigroup → It, The

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Important terminology

semigroup numerical set number frobenius semigroups integers also called integer nonnegative embedding dimension genus denoted generators known positive n2 following

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Numerical semigroupis aspecial kind of a semigroup0.90text
Numerical semigroupis aminimal system of generators if none of its proper subsets generates the numerical semigroup0.90text
Numerical semigroupis anumerical semigroup such that it cannot be written as the intersection of two numerical semigroups properly containing it0.90text
Numerical semigrouprelated to Apéry SetLet0.60section
Numerical semigrouprelated to Apéry SetThe Apéry0.60section
Numerical semigrouprelated to Apéry SetAp0.60section
Numerical semigrouprelated to Apéry SetEquivalently0.60section
Numerical semigrouprelated to Apéry SetTypically0.60section
Numerical semigrouprelated to Apéry SetApéry0.60section
Numerical semigrouprelated to Apéry SetThe Frobenius0.60section
Numerical semigrouprelated to DefinitionLet0.60section
Numerical semigrouprelated to DefinitionSN0.60section

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