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Author : Percy A. MacMahon
Publisher : Unknown
Page : 642 pages
File Size : 42,9 Mb
Release : 1960
Category : Electronic
ISBN : OCLC:310795255
Author : Percy A. MacMahon
Publisher : Unknown
Page : 340 pages
File Size : 52,7 Mb
Release : 2001
Category : Electronic
ISBN : OCLC:699087246
Author : Percy A. MacMahon
Publisher : American Mathematical Society
Page : 684 pages
File Size : 40,9 Mb
Release : 2001-05-14
Category : Mathematics
ISBN : 9780821828328
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.”
Author : Percy A. MacMahon
Publisher : Courier Corporation
Page : 770 pages
File Size : 55,6 Mb
Release : 2004-07-06
Category : Mathematics
ISBN : 0486495868
Account of combinatory analysis theorems shows their connections and unites them as parts of a general doctrine. Topics include symmetric functions, theory of number compositions, more. 1915, 1916, and 1920 editions.
Author : Percy A. Macmahon
Publisher : Forgotten Books
Page : 362 pages
File Size : 46,9 Mb
Release : 2015-06-25
Category : Mathematics
ISBN : 133039058X
Excerpt from Combinatory Analysis, Vol. 2 Volume I of this work will not be found to overlap Netto's Combinatorik to any considerable extent. The latter excellent treatise treats for the most part of combinations of objects which are all different, and deals with many special investigations of interest concerning them. It is particularly good in the historical treatment, and the reader who desires a comprehensive account of combinatory analysis should read the Combinatorik, as well as the present book. Investigations by, amongst other writers, Weyrauch, Longchamp, Tait, Cantor, Terquem, Weiss, Metzler, Sprague, Scheck, Schroder, Steiner, Reiss, Moore, De Vries, Heffter, Kirkman, Lucas, are given by Netto, which are valuable, but are not within the scope of the task undertaken here. This has in view the presentation of processes of great generality, and of new ideas, which have not up to the present time found a place in any book in any language. This second volume commences with a detailed account of what is known concerning the algebra of the Theory of Partitions of Numbers, the point of view being that of Euler, and the first Section overlaps the Combinatorik to some extent. It does not include the investigations of Sylvester and Cayley in regard to expressions for the general coefficients in the enumerating generating functions. These are omitted as being arithmetical rather than algebraical. The reader is recommended to consult the original memoirs, and also a short account in the work of Netto. New ideas will be found in Section VII in regard to: (i) the transformation of certain series by a graphical method; (ii) the discussion of Ramanujan's important identities; (iii) the transformation of certain generating functions by means of symmetric functions; (iv) the connexion of the theory of partitions with other combinatory theories. The most important part of the volume, Sections VIII et seq., arises from basing the theory of partitions upon the theory of Diophantine inequalities. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author : Krishnaswami Alladi,Bruce C. Berndt,Peter Paule,James A. Sellers,Ae Ja Yee
Publisher : Springer Nature
Page : 810 pages
File Size : 47,5 Mb
Release : 2021-02-10
Category : Mathematics
ISBN : 9783030570507
This book presents a printed testimony for the fact that George Andrews, one of the world’s leading experts in partitions and q-series for the last several decades, has passed the milestone age of 80. To honor George Andrews on this occasion, the conference “Combinatory Analysis 2018” was organized at the Pennsylvania State University from June 21 to 24, 2018. This volume comprises the original articles from the Special Issue “Combinatory Analysis 2018 – In Honor of George Andrews’ 80th Birthday” resulting from the conference and published in Annals of Combinatorics. In addition to the 37 articles of the Andrews 80 Special Issue, the book includes two new papers. These research contributions explore new grounds and present new achievements, research trends, and problems in the area. The volume is complemented by three special personal contributions: “The Worlds of George Andrews, a daughter’s take” by Amy Alznauer, “My association and collaboration with George Andrews” by Krishna Alladi, and “Ramanujan, his Lost Notebook, its importance” by Bruce Berndt. Another aspect which gives this Andrews volume a truly unique character is the “Photos” collection. In addition to pictures taken at “Combinatory Analysis 2018”, the editors selected a variety of photos, many of them not available elsewhere: “Andrews in Austria”, “Andrews in China”, “Andrews in Florida”, “Andrews in Illinois”, and “Andrews in India”. This volume will be of interest to researchers, PhD students, and interested practitioners working in the area of Combinatory Analysis, q-Series, and related fields.
Author : Percy Alexander Macmahon
Publisher : Mjp Publishers
Page : 0 pages
File Size : 55,9 Mb
Release : 2023
Category : Fiction
ISBN : 9391270433
Author : Percy Alexander MacMahon
Publisher : Unknown
Page : 0 pages
File Size : 50,8 Mb
Release : 1960
Category : Combinatorial analysis
ISBN : OCLC:1224681519
Author : Percy Alexander Macmahon
Publisher : Andesite Press
Page : 366 pages
File Size : 44,6 Mb
Release : 2015-08-12
Category : Electronic
ISBN : 129675829X
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author : Percy Alexander Macmahon
Publisher : Theclassics.Us
Page : 60 pages
File Size : 46,9 Mb
Release : 2013-09
Category : Electronic
ISBN : 1230735100
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1916 edition. Excerpt: ...coefficients being positive integers, and it also will be a general magic square. An ordinary magic square is a particular case of a general magic square, but the particular property of an ordinary magic square that it must involve different integers in the compartments prevents the formation of new squares by addition, so that within the group of such squares there is no syzygetic theory. 158 THE SYZYGETIC THEORY SECT. VIII 405. We proceed to investigate the syzygetic theory of general magic squares of the Third Order. Such squares do not exist in the case of the Second Order except in the trivial case a a a a but there are squares in which the row and column but not the diagonal properties are in evidence. For let such a square be a1 2 This must clearly have the form a. a. a, a, where if oo be some integer a, +a = a5) and we find S'iZfaf = n.--., wherein we recall that the symbol fl denotes that in the ascending expansion of the function to which it is prefixed we are to retain only those terms which are free from the auxiliary X. The expression clearly has the value (1--XiXil-X2X2)' the denominator factors denoting the fundamental solutions Thus we have the fundamental squares I t) 0 1 0 1 10 and the most general square of the type 1 1 0 10 1 'a, a, ai n l + 0,2 I n-0 1 1 0 I Oj a, a trivial result. (the exponent of xw being unity shewing that the number associated with the rows and columns is unity) connected by the simple syzygy 100 010 001 010 +001 +100 001 100 010 100 010 001 = 001 +100 +010 010 001 100 each side being equal to 1 1 1 1 L J. Xj Xj) Xq X Xg tt-g Xj Xft Xa VUq a 1 1 1 This is the complete syzygetic theory of these squares. CH. VII PROPERTIES OF BOTH DIAGONALS IN EVIDENCE and writing these...
Author : Percy Alexander Macmahon
Publisher : Theclassics.Us
Page : 70 pages
File Size : 45,8 Mb
Release : 2013-09
Category : Electronic
ISBN : 1230735127
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1915 edition. Excerpt: ...that p--r has no longer (the number of different letters exceeding 2) any simple value for different classes of permutations. It is not possible to obtain expressions for %afl and %xp+r in the foregoing manner. 110. The Parity of the Greater Index. The permutations of a" '7... are such that the number with an even index is equal to the number with an uneven index whenever more than one of the numbers k, ... are uneven. Consider the function (l)(2)...(i+j+k +...) (l)(2)...(i)(l)(2)...(j)(l)(2)...(k)...' if we put, therein, x =--1 and the function happens to vanish it must be because the permutations with even index are equal in number to those with uneven index. This is the case because the function is equal to %Gpxp where there are Cp permutations having the index equal to p. Under what conditions does x =--1 cause the function to vanish? The factor (m) becomes 2 for x =--1 whenever m is uneven. Eliminating these factors we are left with a function which may be of the form when x =--1 and can be evaluated. This happens when numerator and denominator contain the same number of factors (to), wherein To is even. If this be not the case the numerator must contain more of such factors than the denominator and the function must vanish for x=--1. Observe that the numerator cannot involve fewer of such factors than the denominator, for in that case the function would become infinite for x =--1, which from the nature of the function is absurd. We have, then, to find out the circumstances under which the numerator of the complete function involves more factors (to) than the denominator, To being even. If we consider the product (1)(2)...() and denote by Ea the greatest integer in a, it will be seen that the number of factors (to), ...
Author : Anonim
Publisher : CUP Archive
Page : 330 pages
File Size : 50,8 Mb
Release : 2024-07-04
Category : Electronic
ISBN : 8210379456XXX
Author : Anonim
Publisher : Univ of California Press
Page : 774 pages
File Size : 48,7 Mb
Release : 2024-07-04
Category : Electronic
ISBN : 9780520325876
Author : Percy Alexander MacMahon
Publisher : CUP Archive
Page : 370 pages
File Size : 41,6 Mb
Release : 1915
Category : Electronic
ISBN : 8210379456XXX
Author : Lucien M. Le Cam,Jerzy Neyman,Elizabeth L. Scott
Publisher : Univ of California Press
Page : 732 pages
File Size : 48,5 Mb
Release : 2024-03-29
Category : Mathematics
ISBN : 9780520375895
This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1972.