Table of Contents

Chapter I

Elementary Theory of Symmetric Functions

art. | page | |

1—3. | Definitions. The Partition Notation. The Power-Sums | 1 |

4—5. | The Elementary Function. Homogeneous Product-Sums | 4 |

6—8. | Relations between the important series of functions | 5 |

9—10. | Combination and Permutation of letters. Partitions and Compositions of numbers | 8 |

11—13. | Order of arrangement of combinations, permutations, partitions and compositions. Dictionary or Alphabetical Order | 8 |

Chapter II

Opening of the Theory of Distributions

14—15. | Definite way of performing algebraical multiplication | 11 |

16—20. | Distribution of letters or objects into boxes. Specifications of objects and boxes. Multinomial Theorem. Distribution Function | 12 |

21—23. | Examples of Distribution. Dual interpretation of Binomial Theorem | 15 |

24—27. | Interpretation of the product of two or more monomial symmetric functions | 17 |

28—29. | The multiplication of symmetric functions. Derivation of formulæ. The symbol of operation | 22 |

30—31. | Operation of upon a product of functions. Connexion with the compositions of | 25 |

Chapter III

Distribution into different boxes

32—33. | Determination of the enumerating function in the case of two boxes | 27 |

34—37. | The general theory of any number of boxes. Operation of upon products of product-sums. Numerical methods and formulæ | 29 |

38—39. | Restriction upon the number of similar objects that may be placed in similar boxes. Operation of in this case | 33 |