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This volume is produced from digital images created through the University of Michigan University Library's preservation reformatting program. ... Read more

Book Description
Percy Alexander Macmahon (1854-1929) was something of an anomaly in the mathematical fraternity of his time. Much of his life was spent in the British military manning the outposts of Empire and teaching in military schools rather than in the established academic preserves. just so, he marched to his own drumbeat in his mathematical researches, and his work was often far ahead of its time. Reviewing Volume I, Combinatorics (1978), in his Scientific American feature column, Martin Gardner noted that "it is remarkable how often results of MacMahon's are rediscovered by mathematicians who until now have not had access to his voluminous writings."

Some of the fifty-six papers in Volume II relate to combinatorics, but most of them investigate quite distinct areas and reveal a different side of MacMahons mind and mathematical originality. They are grouped into chapters that cover symmetric functions of several systems of quantities, determinants, repeating patterns, multiplicative number theory, applications (to analysis, astronomy, geometry, and physics), and invariant theory. A final chapter collects expository papers on such subjects as the state of knowledge of combinatory analysis and magic squares "and other problems upon a chess board."

The editor has provided an introduction and commentary for each of these chapters that bring historical perspective to the papers and relate them to contemporary developments. Summaries of the papers have also been provided.

George E. Andrews is Evan Pugh Professor of Mathematics at Pennsylvania State University. This volume of MacMahons collected papers is the twenty-fourth and final volume in The MIT Press Mathematicians of Our Time series, edited by Gian-Carlo Rota. ... Read more

Book Description
By "combinatory analysis", the author understands the part ofcombinatorics now known as "algebraic combinatorics". In thisbook, the classical results of the outstanding 19th centuryschool of British mathematicians are presented with greatclarity and completeness.

From the Introduction (1915): "The object of this work is, in themain, to present to mathematicians an account of theorems incombinatory analysis which are of a perfectly general character,and to show the connection between them by as far as possiblebringing them together as parts of a general doctrine. It mayappeal also to others whose reading has not been very extensive.They may not improbably find here some new points of view andsuggestions which may prompt them to original investigation in afascinating subject ...

"In the present volume there appears a certain amount of originalmatter which has not before been published. It involves theauthor's preliminary researches in combinatory theory which havebeen carried out during the last thirty years. For the most partit is original work which, however, owes much to valuable papersby Cayley, Sylvester, and Hammond." ... Read more

Book Description

Book Description
An Unabridged Printing Of Volume I, To Include: 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 - The Theory Of Separations - Generalization Of Girard's Formula - The Differential Operators Of The Theory Of Separations - A Calculus Of Binomial Coefficients - The Theory Of Three Identities - The Enumeration Of Permutations - The Theory Of Displacements - Other Applications Of The Master Theorem - Lattice Permutations - The Indices Of Permutations - Unipartite Numbers - Multipartite Numbers The Graphical Representation Of The Compositions Of Tripartite And Multipartite Numbers - Simon Newcomb's Problem - Generalization Of The Foregoing Theory - Distributions Upon A Chessboard, To Which Is Prefixed A Chapter On Perfect Partitions - Theory Of The Perfect Partitions Of Numbers - Arrangements Upon A Chessboard - The Theory Of The Latin Square - Etc, Etc. - Tables ... Read more