## Integer PartitionsThe theory of integer partitions is a subject of enduring interest. A major research area in its own right, it has found numerous applications, and celebrated results such as the Rogers-Ramanujan identities make it a topic filled with the true romance of mathematics.The aim in this introductory textbook is to provide an accessible and wide ranging introduction to partitions, without requiring anything more of the reader than some familiarity with polynomials and infinite series. Many exercises are included, together with some solutions and helpful hints. |

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### Contents

II | ii |

III | 5 |

IV | 6 |

V | 8 |

VI | 10 |

VII | 14 |

VIII | 15 |

IX | 16 |

XXXI | 69 |

XXXII | 71 |

XXXIII | 74 |

XXXIV | 75 |

XXXV | 78 |

XXXVI | 79 |

XXXVII | 81 |

XXXVIII | 85 |

### Common terms and phrases

3-distinct arctic circle theorem Aztec diamond bijective proof binomial numbers binomial series binomial theorem Chapter coefficients column combinatorial computers congruent conjugation consecutive multiples construct converges Difficulty rating domino tilings elements equals the number Euler pair Euler's identity Euler's pentagonal number example Ferrers graph Fibonacci numbers four partitions Frobenius symbols function for partitions Gaussian polynomials hall partition theorem Hasse diagram Hence hook length formula inner corner integer partitions l-part largest lecture hall partition mathematical induction mathematicians number of dots number of odd number of partitions number of standard odd distinct odd number partition function partition identity partition into distinct partition of length partitions into odd pentagonal number theorem plane partitions positive integers Ramanujan recursion reduced lecture hall result Rogers-Ramanujan identity Schur self-conjugate sequence set of partitions show that p(n smallest splitting standard tableaux step successive Durfee squares super-distinct theory of partitions transformation unique usual order