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 |