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Contents

viii

Chapter IV

Distribution when Objects and Boxes are equal in number

art. | page | |

40—42. | Solution by means of product-sums. Interchange of Specification of Objects and Boxes. Theorem of symmetry in the algebra of product-sums. Employment of the symbol | 36 |

43—47. | Pairing of objects of two different sets of objects. Specification of a distribution. Restriction upon the number of similar objects that can be placed in similar boxes. The operation of | 38 |

48—49. | Enumeration of rectangular diagrams involving compositions of numbers | 42 |

50—51. | Equivalences of certain distributions | 44 |

Chapter V

Distributions of given specification

52—58. | New functions which put the specification of a distribution in evidence. Proof of symmetry in the functions. Separation of a function or of a partition. Solution of the problem of enumeration. Operation of upon the new functions. An example of enumeration | 46 |

59—61. | Correspondence with numbered diagrams | 52 |

Chapter VI

The most general case of Distribution

62—74. | Distribution when the boxes are identical. Multipartite numbers and their partitions. Distribution into similar boxes identified with the partitions of multipartite numbers. Solution of the problem by means of product-sums of certain combinations. Application of symbol . Simple particular cases | 56 |

75—77. | The most general case of distribution. Application to the distribution of identical objects. Elegant theorem of distribution which depends upon conjugate partitions. Some particular examples and verifications | 65 |

78—81. | Certain restricted distributions | 67 |