"several equivalent ways of forming the graphical representation"

The theory of partitions (Encyclopedia of mathematics and its applications ; v. 2 : Section, Number theory)

Reference

Andrews, George E.

Encyclopedias & Subject Guides

Longman Higher Education

This first volume of the collected papers of MacMahon is a member of the series Mathematicians of Our Time and takes its place among the previously published collections of the work of Paul Erdös, Einar Hille, Charles Loewner, George Pólya, Hans Rademacher, Stanislaw Ulam, Norbert Wiender, and Oscar Zariski. Gian-Carlo Rota, Professor of Mathematics at MIT, is founding editor of the series. George E. Andrews, the editor of this and a subsequent volume that together contain MacMahon's major papers, writes that "there are several compelling reasons for publishing the Collected Papers of Percy Alexander MacMahon (1854-1929): "First, MacMahon's researches in combinatorics were ahead of his time. In studying the literature of MacMahon's day, we find that while MacMahon was a prolific writer (as these Collected Papers confirm), his discoveries generated little work by others on combinatorics. Within the past twenty years, however, combinatorics has undergone a remarkable renaissance, and a random check through the Science Citation Index indicates clearly that MacMahon's work is no longer neglected. "Second, well over twenty-five percent of MacMahon's papers appeared after the publication of his historic two volume work, Combinatory Analysis |1915, 1916|.... This later work includes his extensive researches on determinants, his book and papers on repeating patterns, and numerous contributions to combinatorics, notably his enumeration of the partitions of a multipartite number. Furthermore, less than twenty percent of all his papers are referred to in Combinatory Analysis; the impact of Combinatory Analysis alone on the contemporary scientific community suggests the importance of publishing all MacMahon's papers...." The papers in this first volume are grouped by subject area: symmetric functions (18 papers), the Master Theorem (2 papers), permutations (9 papers), compositions and Simon Newcomb's problem (4 papers), perfect partitions (4 papers), distributions upon a chess board and Latin Squares (3 papers), multipartite numbers (5 papers), partitions (6 papers), partition analysis (9 papers), and plane and solid partitions (4 papers). This sequence of topics closely parallels the thematic development of MacMahon's Combinatory Analysis. Each topical group is preceded by an introduction and commentary that relates the papers to contemporary developments, a summary of each of the papers, and in two chapters, additional commentary in the form of related papers by other mathematicians, namely, P. Hall and D. E. Littlewood.

Percy Alexander Macmahon: Collected Papers (Mathematicians of Our Time, V. 13, 24.)

Science & Math

MacMahon, Percy Alexander

Mathematics

Mit Pr

LPAR is an international conference series aimed at bringing together researchers interested in logic programming and automated reasoning. The research in logic programming grew out of the research in automated reasoning in the early 1970s. Later, the implementation techniques known from logic programming were used in implementing theorem proving systems. Results from both fields applied to deductive databases. This volume contains the proceedings of LPAR '93, which was organized by the Russian Association for Logic Programming. The volume contains 35 contributed papers selected from 84 submissions, together with an invited paper by Peter Wegner entitled "Reasoning versus modeling in computer science".

Logic Programming and Automated Reasoning: 4th International Conference, Lpar '93 St. Petersburg, Russia, July 13-20, 1993 Proceedings (Lecture Notes in Computer Science 698)

Computers & Technology

Berndt, Bruce C.

Computer Science

Springer

In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated "Ramanujan's lost notebook." The "lost notebook" contains considerable material on mock theta functions and so undoubtedly emanates from the last year of Ramanujan's life. It should be emphasized that the material on mock theta functions is perhaps Ramanujan's deepest work.

Ramanujan's Lost Notebook: Part II

Biographies & Memoirs

The theory of integer partitions is a subject of enduring interest as well as a major research area. It has found numerous applications, including celebrated results such as the Rogers-Ramanujan identities. The aim of this introductory textbook is to provide an accessible and wide-ranging introduction to partitions, without requiring anything more than some familiarity with polynomials and infinite series. Many exercises are included, together with some solutions and helpful hints.

Integer Partitions ICM Edition

Eriksson, Kimmo

Cambridge University Press

This volume presents an overview of the area of special functions, focusing primarily on the hypergeometric functions and the associated hypergeometric series.

Special Functions ICM Edition (Encyclopedia of Mathematics and its Applications, Series Number 71)

Askey, Richard

Roy, Ranjan

The Theory of Partitions (Encyclopedia of Mathematics and its Applications, Series Number 2)

This book develops the theory of partitions. Simply put, the partitions of a number are the ways of writing that number as sums of positive integers. For example, the five partitions of 4 are 4, 3+1, 2+2, 2+1+1, and 1+1+1+1. Surprisingly, such a simple matter requires some deep mathematics for its study. This book considers the many theoretical aspects of this subject, which have in turn recently found applications to statistical mechanics, computer science and other branches of mathematics. With minimal prerequisites, this book is suitable for students as well as researchers in combinatorics, analysis, and number theory.

Special Functions (Encyclopedia of Mathematics and its Applications, Series Number 71)

Special functions, which include the trigonometric functions, have been used for centuries. Their role in the solution of differential equations was exploited by Newton and Leibniz, and the subject of special functions has been in continuous development ever since. In just the past thirty years several new special functions and applications have been discovered. This treatise presents an overview of the area of special functions, focusing primarily on the hypergeometric functions and the associated hypergeometric series. It includes both important historical results and recent developments and shows how these arise from several areas of mathematics and mathematical physics. Particular emphasis is placed on formulas that can be used in computation. The book begins with a thorough treatment of the gamma and beta functions that are essential to understanding hypergeometric functions. Later chapters discuss Bessel functions, orthogonal polynomials and transformations, the Selberg integral and its applications, spherical harmonics, q-series, partitions, and Bailey chains. This clear, authoritative work will be a lasting reference for students and researchers in number theory, algebra, combinatorics, differential equations, applied mathematics, mathematical computing, and mathematical physics.

Integer Partitions

The theory of integer partitions is a subject of enduring interest as well as a major research area. It has found numerous applications, including celebrated results such as the Rogers-Ramanujan identities. The aim of this introductory textbook is to provide an accessible and wide-ranging introduction to partitions, without requiring anything more than some familiarity with polynomials and infinite series. Many exercises are included, together with some solutions and helpful hints.

See the best price to sell, buy, or rent books by Andrews, George E.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Andrews, George E.

See the best price to sell, buy, or rent books by Andrews, George E.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

The theory of partitions (Encyclopedia of mathematics and its applications ; v. 2 : Section, Number theory)

Percy Alexander Macmahon: Collected Papers (Mathematicians of Our Time, V. 13, 24.)

Logic Programming and Automated Reasoning: 4th International Conference, Lpar '93 St. Petersburg, Russia, July 13-20, 1993 Proceedings (Lecture Notes in Computer Science 698)

Ramanujan's Lost Notebook: Part II

Integer Partitions ICM Edition

Special Functions ICM Edition (Encyclopedia of Mathematics and its Applications, Series Number 71)

The Theory of Partitions (Encyclopedia of Mathematics and its Applications, Series Number 2)

Special Functions (Encyclopedia of Mathematics and its Applications, Series Number 71)

The Theory of Partitions (Encyclopedia of Mathematics and its Applications, Series Number 2)

Integer Partitions