### Abstract

K. Alladi first observed the following 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. Subsequently, the theorem was refined to count also the number of parts in the relevant partitions. In this paper, a surprising factorization of the related polynomial generating functions is developed.

Original language | English (US) |
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Title of host publication | Analytic Number Theory, Modular Forms and q-Hypergeometric Series - In Honor of Krishna Alladi’s 60th Birthday, 2016 |

Editors | George E. Andrews, Frank Garvan |

Publisher | Springer New York LLC |

Pages | 25-38 |

Number of pages | 14 |

ISBN (Print) | 9783319683751 |

DOIs | |

State | Published - Jan 1 2017 |

Event | International Gainesville Number Theory Conference in Honor of Krishna Alladi’s 60th Birthday, 2016 - Gainesville, United States Duration: Mar 17 2016 → Mar 21 2016 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 221 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Other

Other | International Gainesville Number Theory Conference in Honor of Krishna Alladi’s 60th Birthday, 2016 |
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Country | United States |

City | Gainesville |

Period | 3/17/16 → 3/21/16 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Analytic Number Theory, Modular Forms and q-Hypergeometric Series - In Honor of Krishna Alladi’s 60th Birthday, 2016*(pp. 25-38). (Springer Proceedings in Mathematics and Statistics; Vol. 221). Springer New York LLC. https://doi.org/10.1007/978-3-319-68376-8_3

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*Analytic Number Theory, Modular Forms and q-Hypergeometric Series - In Honor of Krishna Alladi’s 60th Birthday, 2016.*Springer Proceedings in Mathematics and Statistics, vol. 221, Springer New York LLC, pp. 25-38, International Gainesville Number Theory Conference in Honor of Krishna Alladi’s 60th Birthday, 2016, Gainesville, United States, 3/17/16. https://doi.org/10.1007/978-3-319-68376-8_3

**The Alladi–Schur polynomials and their factorization.** / Andrews, George E.

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

TY - GEN

T1 - The Alladi–Schur polynomials and their factorization

AU - Andrews, George E.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - K. Alladi first observed the following 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. Subsequently, the theorem was refined to count also the number of parts in the relevant partitions. In this paper, a surprising factorization of the related polynomial generating functions is developed.

AB - K. Alladi first observed the following 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. Subsequently, the theorem was refined to count also the number of parts in the relevant partitions. In this paper, a surprising factorization of the related polynomial generating functions is developed.

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UR - http://www.scopus.com/inward/citedby.url?scp=85042126119&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-68376-8_3

DO - 10.1007/978-3-319-68376-8_3

M3 - Conference contribution

AN - SCOPUS:85042126119

SN - 9783319683751

T3 - Springer Proceedings in Mathematics and Statistics

SP - 25

EP - 38

BT - Analytic Number Theory, Modular Forms and q-Hypergeometric Series - In Honor of Krishna Alladi’s 60th Birthday, 2016

A2 - Andrews, George E.

A2 - Garvan, Frank

PB - Springer New York LLC

ER -