Young diagrams
E924200
Young diagrams are combinatorial diagrams consisting of left-justified rows of boxes that visually represent integer partitions and play a central role in the representation theory of symmetric and general linear groups.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Young diagrams canonical | 3 |
| Ferrers graph | 1 |
| Young tableaux | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11411665 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Young diagrams Context triple: [Gelfand–Tsetlin basis, relatedTo, Young diagrams]
-
A.
Coxeter–Dynkin diagrams
Coxeter–Dynkin diagrams are graphical representations that encode the structure of reflection groups and root systems, widely used in the classification of regular polytopes, Lie algebras, and symmetries.
-
B.
Gelfand–Tsetlin basis
The Gelfand–Tsetlin basis is a canonical, combinatorially defined basis for representations of certain Lie algebras and groups, particularly used in the representation theory of GL(n) and related structures.
-
C.
Schur–Weyl duality
Schur–Weyl duality is a fundamental result in representation theory that links representations of the symmetric group and the general linear group via their commuting actions on tensor powers of a vector space.
-
D.
Macdonald polynomials
Macdonald polynomials are a family of orthogonal symmetric functions depending on two parameters that generalize several classical symmetric polynomials, such as Schur and Jack polynomials, and play a central role in algebraic combinatorics and representation theory.
-
E.
Sylvester’s theorem on partitions
Sylvester’s theorem on partitions is a result in number theory that provides a systematic way to count integer partitions subject to certain congruence or restriction conditions, forming part of the foundational work in partition theory.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Young diagrams Target entity description: Young diagrams are combinatorial diagrams consisting of left-justified rows of boxes that visually represent integer partitions and play a central role in the representation theory of symmetric and general linear groups.
-
A.
Coxeter–Dynkin diagrams
Coxeter–Dynkin diagrams are graphical representations that encode the structure of reflection groups and root systems, widely used in the classification of regular polytopes, Lie algebras, and symmetries.
-
B.
Gelfand–Tsetlin basis
The Gelfand–Tsetlin basis is a canonical, combinatorially defined basis for representations of certain Lie algebras and groups, particularly used in the representation theory of GL(n) and related structures.
-
C.
Schur–Weyl duality
Schur–Weyl duality is a fundamental result in representation theory that links representations of the symmetric group and the general linear group via their commuting actions on tensor powers of a vector space.
-
D.
Macdonald polynomials
Macdonald polynomials are a family of orthogonal symmetric functions depending on two parameters that generalize several classical symmetric polynomials, such as Schur and Jack polynomials, and play a central role in algebraic combinatorics and representation theory.
-
E.
Sylvester’s theorem on partitions
Sylvester’s theorem on partitions is a result in number theory that provides a systematic way to count integer partitions subject to certain congruence or restriction conditions, forming part of the foundational work in partition theory.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
combinatorial object
ⓘ
diagram ⓘ |
| associatedWith |
Schur functions
ⓘ
Young tableaux ⓘ semistandard Young tableaux ⓘ standard Young tableaux ⓘ symmetric functions ⓘ |
| conjugationActsOn | integer partitions ⓘ |
| conjugationCorrespondsTo | transposing rows and columns ⓘ |
| correspondsTo |
Ferrers diagram
ⓘ
partition written in nonincreasing order ⓘ |
| embeddedIn | integer lattice grid ⓘ |
| hasOperation |
conjugation
ⓘ
transpose ⓘ |
| hasParameter |
column lengths
ⓘ
number of boxes ⓘ row lengths ⓘ |
| hasProperty |
consists of unit boxes (cells)
ⓘ
rows are arranged in nonincreasing order of length ⓘ rows are left-justified ⓘ |
| hasVariant |
border strip diagram
ⓘ
shifted Young diagram ⓘ skew Young diagram ⓘ |
| introducedBy | Alfred Young ⓘ |
| orientation |
columns extend downward from the top row
ⓘ
rows extend to the right from the left margin ⓘ |
| relatedTo |
Ferrers graph
ⓘ
linked to:
Young diagrams
hook-length formula ⓘ |
| represents | integer partition ⓘ |
| usedIn |
Littlewood–Richardson rule
ⓘ
algebraic combinatorics ⓘ branching rules for general linear groups ⓘ branching rules for symmetric groups ⓘ combinatorial representation theory ⓘ general linear group representation theory ⓘ representation theory ⓘ symmetric function theory ⓘ symmetric group representation theory ⓘ |
| usedToCount | standard Young tableaux ⓘ |
| usedToDescribe |
Young subgroup decompositions
ⓘ
Young symmetrizers ⓘ hook-length formula applications ⓘ |
| usedToIndex |
Schur functors
ⓘ
Specht modules ⓘ irreducible representations of symmetric groups ⓘ polynomial representations of general linear groups ⓘ |
| visualizes | partition of a positive integer ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Young diagrams Description of subject: Young diagrams are combinatorial diagrams consisting of left-justified rows of boxes that visually represent integer partitions and play a central role in the representation theory of symmetric and general linear groups.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject linked to:
Richard Stanley
linked to: Young diagrams
subject linked to:
Young diagrams
linked to: Young diagrams