Page:An introduction to Combinatory analysis (Percy MacMahon, 1920, IA Introductiontoco00macmrich).djvu/13

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 $D_{m}$	22
30—31.	Operation of $D_{m}$ upon a product of functions. Connexion with the compositions of $m$	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 $D_{m}$ 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 $D_{m}$ in this case	33