Sylvester’s theorem on partitions
E571007
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Sylvester’s theorem on partitions canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6149925 — 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: Sylvester’s theorem on partitions Context triple: [James Joseph Sylvester, notableWork, Sylvester’s theorem on partitions]
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A.
Ramanujan partition congruences
Ramanujan partition congruences are remarkable number-theoretic results discovered by Srinivasa Ramanujan that describe surprising modular patterns in the partition function, such as specific arithmetic progressions where the number of integer partitions of an integer is divisible by a given prime.
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B.
Ono’s partition congruences
Ono’s partition congruences are modern number-theoretic results that extend Ramanujan’s classical congruences by proving the existence of infinitely many congruence relations for the partition function modulo various primes.
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C.
Hardy–Ramanujan asymptotic formula
The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
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D.
Minkowski’s theorem on convex sets
Minkowski’s theorem on convex sets is a fundamental result in convex geometry that characterizes lattice points in convex bodies, underpinning much of the theory of convex polytopes and the geometry of numbers.
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E.
Fermat polygonal number theorem
The Fermat polygonal number theorem is a result in number theory stating that every positive integer can be expressed as a sum of a fixed number of polygonal numbers of a given order.
- 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: Sylvester’s theorem on partitions Target entity description: 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.
-
A.
Ramanujan partition congruences
Ramanujan partition congruences are remarkable number-theoretic results discovered by Srinivasa Ramanujan that describe surprising modular patterns in the partition function, such as specific arithmetic progressions where the number of integer partitions of an integer is divisible by a given prime.
-
B.
Ono’s partition congruences
Ono’s partition congruences are modern number-theoretic results that extend Ramanujan’s classical congruences by proving the existence of infinitely many congruence relations for the partition function modulo various primes.
-
C.
Hardy–Ramanujan asymptotic formula
The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
-
D.
Minkowski’s theorem on convex sets
Minkowski’s theorem on convex sets is a fundamental result in convex geometry that characterizes lattice points in convex bodies, underpinning much of the theory of convex polytopes and the geometry of numbers.
-
E.
Fermat polygonal number theorem
The Fermat polygonal number theorem is a result in number theory stating that every positive integer can be expressed as a sum of a fixed number of polygonal numbers of a given order.
- F. None of above. chosen
Statements (25)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theorem
ⓘ
result in number theory ⓘ |
| appliesTo |
partitions with congruence constraints
ⓘ
restricted integer partitions ⓘ |
| contributesTo | foundations of partition theory ⓘ |
| describes |
systematic counting of integer partitions under congruence conditions
ⓘ
systematic counting of integer partitions under restriction conditions ⓘ |
| field |
number theory
ⓘ
partition theory ⓘ |
| hasConcept |
congruence classes of parts in partitions
ⓘ
generating functions for partitions ⓘ restricted partition functions ⓘ |
| hasInfluenced |
development of systematic methods for counting restricted partitions
ⓘ
later work on partition congruences ⓘ |
| hasMathematician | James Joseph Sylvester NERFINISHED ⓘ |
| historicalPeriod | 19th century mathematics ⓘ |
| isPartOf | classical results in partition theory ⓘ |
| mainSubject | integer partitions ⓘ |
| namedAfter | James Joseph Sylvester NERFINISHED ⓘ |
| relatedTo |
combinatorial number theory
ⓘ
partition generating functions ⓘ partition identities ⓘ |
| topicOf | research in additive number theory ⓘ |
| usedFor |
deriving formulas for restricted partition numbers
ⓘ
enumeration of partitions with specified residue classes ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Sylvester’s theorem on partitions Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.