The number of smallest parts in the partitions of n

George E. Andrews

doi:10.1515/CRELLE.2008.083

The number of smallest parts in the partitions of n

George E. Andrews

Mathematics

Research output: Contribution to journal › Article › peer-review

110 Scopus citations

Abstract

We denote by spt(n) the total number of appearances of the smallest part in each integer partition of n. We shall relate spt(n) to the Atkin-Garvan moments of ranks, and we shall prove that 5 | spt(5n + 4), 7 | spt(7n + 5) and 13 | spt(13n + 6).

Original language	English (US)
Pages (from-to)	133-142
Number of pages	10
Journal	Journal fur die Reine und Angewandte Mathematik
Issue number	624
DOIs	https://doi.org/10.1515/CRELLE.2008.083
State	Published - Nov 2008

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1515/CRELLE.2008.083

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title = "The number of smallest parts in the partitions of n",

abstract = "We denote by spt(n) the total number of appearances of the smallest part in each integer partition of n. We shall relate spt(n) to the Atkin-Garvan moments of ranks, and we shall prove that 5 | spt(5n + 4), 7 | spt(7n + 5) and 13 | spt(13n + 6).",

author = "Andrews, {George E.}",

note = "Funding Information: Partially supported by National Science Foundation Grant DMS 0457003.",

year = "2008",

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doi = "10.1515/CRELLE.2008.083",

language = "English (US)",

pages = "133--142",

journal = "Journal fur die Reine und Angewandte Mathematik",

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The number of smallest parts in the partitions of n

Abstract

All Science Journal Classification (ASJC) codes

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