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

Title	An introduction to Combinatory analysis
Author	Percy Alexander MacMahon
Year	1920
Publisher	Cambridge [Eng.] The University press
Source	djvu
Progress	To be proofread
Transclusion	Index not transcluded or unreviewed
OCLC	1047475007

Pages   (key to Page Status)   

- - - - - -  Half-title  ii  Title  iv  v  vi  vii  viii 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 - - - - - - -

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

Chapter IV

Distribution when Objects and Boxes are equal in number

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 $D_{m}$	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 $D_{m}$	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 $D_{m}$ 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 $D_{m}$. 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