Dyson’s transform in number theory
E17018
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
Aliases (2)
- Dyson’s transform ×25
- Freeman Dyson ×3
Statements (28)
| Predicate | Object |
|---|---|
| instanceOf |
combinatorial technique
→
construction in partition theory → tool in additive number theory → |
| appliesTo |
integer partitions
→
|
| context |
theory of integer partitions
→
|
| field |
combinatorics
→
mathematical physics → number theory → number theory → |
| goal |
to construct explicit correspondences between partition sets
→
to obtain combinatorial interpretations of analytic identities → |
| introducedBy |
Freeman Dyson
→
|
| involves |
mapping partitions to other partitions
→
preserving combinatorial statistics under transformation → |
| knownFor |
introducing Dyson’s transform in partition theory
→
|
| methodType |
bijective technique
→
combinatorial transformation → |
| namedAfter |
Freeman Dyson
→
|
| notableFor |
use in proofs of partition congruences
→
|
| purpose |
to manipulate integer partitions
→
to relate different families of partitions → to study partition congruences → to study partition identities → |
| relatedTo |
Dyson’s rank of a partition
→
Ramanujan partition congruences → Rogers–Ramanujan-type identities → |
| usedIn |
analysis of partition generating functions
→
combinatorial proofs of partition theorems → |
Referenced by (1)
| Subject (surface form when different) | Predicate |
|---|---|
|
Freeman Dyson
→
|
notableWork |