### Abstract

Let S denote a subset of the positive integers, and let p_{S}(n) be the associated partition function, that is, p_{S}(n) denotes the number of partitions of the positive integer n into parts taken from S. Thus, if S is the set of positive integers, then p_{S}(n) is the ordinary partition function p(n). In this paper, working in the ring of formal power series in one variable over the field of two elements Z/2Z, we develop new methods for deriving lower bounds for both the number of even values and the number of odd values taken by p_{S}(n), for n ≤ N. New very general theorems are obtained, and applications are made to several partition functions.

Original language | English (US) |
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Pages (from-to) | 437-459 |

Number of pages | 23 |

Journal | International Journal of Mathematics |

Volume | 14 |

Issue number | 4 |

DOIs | |

State | Published - Jun 1 2003 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

*International Journal of Mathematics*,

*14*(4), 437-459. https://doi.org/10.1142/S0129167X03001740