AMS Chelsea Publishing 1960; 642 pp; hardcover Volume: 137 Reprint/Revision History: third printing with corrections 1984; first AMS printing 2001 ISBN10: 0821828320 ISBN13: 9780821828328 List Price: US$50 Member Price: US$45 Order Code: CHEL/137.H
 By "combinatory analysis", the author understands the part of combinatorics now known as "algebraic combinatorics". In this book, the classical results of the outstanding 19th century school of British mathematicians are presented with great clarity and completeness. From the Introduction (1915): "The object of this work is, in the main, to present to mathematicians an account of theorems in combinatory analysis which are of a perfectly general character, and to show the connection between them by as far as possible bringing them together as parts of a general doctrine. It may appeal also to others whose reading has not been very extensive. They may not improbably find here some new points of view and suggestions which may prompt them to original investigation in a fascinating subject ... "In the present volume there appears a certain amount of original matter which has not before been published. It involves the author's preliminary researches in combinatory theory which have been carried out during the last thirty years. For the most part it is original work which, however, owes much to valuable papers by Cayley, Sylvester, and Hammond." Readership Graduate students and research mathematicians. Table of Contents Section I. Symmetric Functions  Elementary theory
 Connexion with the theory of distributions
 The distribution into parcels and groups in general
 The operators of the theory of distributions
 Applications of the operators \(d\) and \(D\)
Section II. Generalization of the Theory of Section I  The theory of separations
 Generalization of Waring's formula
 The differential operators of the theory of separations
 A calculus of binomial coefficients
 The theory of three identities
Section III. Permutations  The enumeration of permutations
 The theory of permutations
 The theory of displacements
 Other applications of the master theorem
 Lattice permutations
 The indices of permutations
Section IV. Theory of the Compositions of Numbers  Unipartite numbers
 Multipartite numbers
 The graphical representation of the compositions of tripartite and multipartite numbers
 Simon Newcomb's problem
 Generalization of the foregoing theory
Section V. Distributions Upon a Chess Board, to Which is Prefixed a Chapter on Perfect Partitions  Theory of the perfect partitions of numbers
 Arrangements upon a chess board
 The theory of the latin square
Section VI. The Enumeration of the Partitions of Multipartite Numbers  Bipartite numbers
 Tripartite and other multipartite numbers
 Tables
