### Abstract

K. Alladi first observed a variant of I. Schur’s 1926 partition theorem. Namely, the number of partitions of n in which all parts are odd and none appears more than twice equals the number of partitions of n in which all parts differ by at least 3 and more than 3 if one of the parts is a multiple of 3. In this paper, we refine this result to one that counts the number of parts in the relevant partitions.

Original language | English (US) |
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Title of host publication | Developments in Mathematics |

Publisher | Springer New York LLC |

Pages | 71-77 |

Number of pages | 7 |

DOIs | |

State | Published - Jan 1 2019 |

### Publication series

Name | Developments in Mathematics |
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Volume | 58 |

ISSN (Print) | 1389-2177 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Developments in Mathematics*(pp. 71-77). (Developments in Mathematics; Vol. 58). Springer New York LLC. https://doi.org/10.1007/978-3-030-11102-1_5

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*Developments in Mathematics.*Developments in Mathematics, vol. 58, Springer New York LLC, pp. 71-77. https://doi.org/10.1007/978-3-030-11102-1_5

**A refinement of the alladi–schur theorem.** / Andrews, George E.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - A refinement of the alladi–schur theorem

AU - Andrews, George E.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - K. Alladi first observed a variant of I. Schur’s 1926 partition theorem. Namely, the number of partitions of n in which all parts are odd and none appears more than twice equals the number of partitions of n in which all parts differ by at least 3 and more than 3 if one of the parts is a multiple of 3. In this paper, we refine this result to one that counts the number of parts in the relevant partitions.

AB - K. Alladi first observed a variant of I. Schur’s 1926 partition theorem. Namely, the number of partitions of n in which all parts are odd and none appears more than twice equals the number of partitions of n in which all parts differ by at least 3 and more than 3 if one of the parts is a multiple of 3. In this paper, we refine this result to one that counts the number of parts in the relevant partitions.

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UR - http://www.scopus.com/inward/citedby.url?scp=85062909430&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-11102-1_5

DO - 10.1007/978-3-030-11102-1_5

M3 - Chapter

AN - SCOPUS:85062909430

T3 - Developments in Mathematics

SP - 71

EP - 77

BT - Developments in Mathematics

PB - Springer New York LLC

ER -