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Rank of a partition — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Rank_of_a_partition
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T23:10:36.045Z
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Rank of a partition — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Rank_of_a_partition (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_137db090bc70 (Metraipolis archive dc_137db090bc70, sha256 336a91cc6806044c8fefa5d115a88dad96a40443b47fcac19b03bdaae5d87e51)

BibTeX

@misc{dc137db090bc70,
  title = {Rank of a partition — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Rank_of_a_partition},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_137db090bc70; sha256 336a91cc6806044c8fefa5d115a88dad96a40443b47fcac19b03bdaae5d87e51},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Rank_of_a_partition. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In number theory and combinatorics, the rank of an integer partition is a certain number associated with the partition. In fact at least two different definitions of rank appear in the literature. The first definition, with which most of this article is concerned, is that the rank of a partition is the number obtained by subtracting the number of parts in the partition from the largest part in the partition. The concept was introduced by Freeman Dyson in a paper published in the journal Eureka. It was presented in the context of a study of certain congruence properties of the partition function discovered by the Indian mathematical genius Srinivasa Ramanujan. A different concept, sharing the same name, is used in combinatorics, where the rank is taken to be the size of the Durfee square of the partition.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «number theory»).
Fonte: Wikipedia in inglese, voce «Rank of a partition» — https://en.wikipedia.org/wiki/Rank_of_a_partition
Wikidata Q7293214 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q7293214
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Rank_of_a_partition?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1378437304, consultata il 2026-10-07T22:48:55.267Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: b71f73862e1b835309af095b5f5a603d91da9dc64f8d576a08799b4ce5f84815