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In mathematics, particularly in the fields of number theory and combinatorics, the rank of a partition of a positive integer is a certain integer 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

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  • Rank of a partition (en)
  • Rango de una partición (es)
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  • En matemáticas, particularmente en los campos de la teoría de números y la combinatoria, el rango de una partición de un entero positivo es un cierto entero asociado con la partición. De hecho, al menos se manejan dos definiciones diferentes en la bibliografía más usual. La primera definición, que concierne a la mayor parte de este artículo, es que el rango de una partición, es el número obtenido restando el número de partes en la partición, de la parte más grande de la partición. El concepto fue introducido por Freeman Dyson en un artículo publicado en la revista Eureka.​ Fue presentado en el contexto de un estudio de ciertas propiedades de congruencia de la función de partición descubierta por el genio matemático indio Srinivasa Ramanujan. Se utiliza un concepto diferente, que comparte e (es)
  • In mathematics, particularly in the fields of number theory and combinatorics, the rank of a partition of a positive integer is a certain integer 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 (en)
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  • En matemáticas, particularmente en los campos de la teoría de números y la combinatoria, el rango de una partición de un entero positivo es un cierto entero asociado con la partición. De hecho, al menos se manejan dos definiciones diferentes en la bibliografía más usual. La primera definición, que concierne a la mayor parte de este artículo, es que el rango de una partición, es el número obtenido restando el número de partes en la partición, de la parte más grande de la partición. El concepto fue introducido por Freeman Dyson en un artículo publicado en la revista Eureka.​ Fue presentado en el contexto de un estudio de ciertas propiedades de congruencia de la función de partición descubierta por el genio matemático indio Srinivasa Ramanujan. Se utiliza un concepto diferente, que comparte el mismo nombre, en combinatoria, donde se toma el rango como el tamaño del de la partición. (es)
  • In mathematics, particularly in the fields of number theory and combinatorics, the rank of a partition of a positive integer is a certain integer 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. (en)
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