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Author: Dominique Foata Publisher: Springer Science & Business Media ISBN: 3642565131 Category : Mathematics Languages : en Pages : 430
Book Description
This book contains seventeen contributions made to George Andrews on the occasion of his sixtieth birthday, ranging from classical number theory (the theory of partitions) to classical and algebraic combinatorics. Most of the papers were read at the 42nd session of the Sminaire Lotharingien de Combinatoire that took place at Maratea, Basilicata, in August 1998. This volume contains a long memoir on Ramanujan's Unpublished Manuscript and the Tau functions studied with a contemporary eye, together with several papers dealing with the theory of partitions. There is also a description of a maple package to deal with general q-calculus. More subjects on algebraic combinatorics are developed, especially the theory of Kostka polynomials, the ice square model, the combinatorial theory of classical numbers, a new approach to determinant calculus.
Author: Dominique Foata Publisher: Springer Science & Business Media ISBN: 3642565131 Category : Mathematics Languages : en Pages : 430
Book Description
This book contains seventeen contributions made to George Andrews on the occasion of his sixtieth birthday, ranging from classical number theory (the theory of partitions) to classical and algebraic combinatorics. Most of the papers were read at the 42nd session of the Sminaire Lotharingien de Combinatoire that took place at Maratea, Basilicata, in August 1998. This volume contains a long memoir on Ramanujan's Unpublished Manuscript and the Tau functions studied with a contemporary eye, together with several papers dealing with the theory of partitions. There is also a description of a maple package to deal with general q-calculus. More subjects on algebraic combinatorics are developed, especially the theory of Kostka polynomials, the ice square model, the combinatorial theory of classical numbers, a new approach to determinant calculus.
Author: V. Sidoravicius Publisher: American Mathematical Soc. ISBN: 1470422484 Category : Mathematics Languages : en Pages : 482
Book Description
This book brings a reader to the cutting edge of several important directions of the contemporary probability theory, which in many cases are strongly motivated by problems in statistical physics. The authors of these articles are leading experts in the field and the reader will get an exceptional panorama of the field from the point of view of scientists who played, and continue to play, a pivotal role in the development of the new methods and ideas, interlinking it with geometry, complex analysis, conformal field theory, etc., making modern probability one of the most vibrant areas in mathematics.
Author: Alain Lascoux Publisher: American Mathematical Soc. ISBN: 9780821889435 Category : Science Languages : en Pages : 282
Book Description
The theory of symmetric functions is an old topic in mathematics which is used as an algebraic tool in many classical fields. With $\lambda$-rings, one can regard symmetric functions as operators on polynomials and reduce the theory to just a handful of fundamental formulas. One of the main goals of the book is to describe the technique of $\lambda$-rings. The main applications of this technique to the theory of symmetric functions are related to the Euclid algorithm and itsoccurrence in division, continued fractions, Pade approximants, and orthogonal polynomials. Putting the emphasis on the symmetric group instead of symmetric functions, one can extend the theory to non-symmetric polynomials, with Schur functions being replaced by Schubert polynomials. In two independentchapters, the author describes the main properties of these polynomials, following either the approach of Newton and interpolation methods or the method of Cauchy. The last chapter sketches a non-commutative version of symmetric functions, using Young tableaux and the plactic monoid. The book contains numerous exercises clarifying and extending many points of the main text. It will make an excellent supplementary text for a graduate course in combinatorics.
Author: Bernhard Krötz Publisher: Springer Science & Business Media ISBN: 081764816X Category : Mathematics Languages : en Pages : 282
Book Description
This volume targets graduate students and researchers in the fields of representation theory, automorphic forms, Hecke algebras, harmonic analysis, number theory.
Author: Ranjan Roy Publisher: Cambridge University Press ISBN: 1108573185 Category : Mathematics Languages : en Pages :
Book Description
This is the first volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible to even advanced undergraduate students, discusses the development of the methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 treats more recent work, including deBranges' solution of Bieberbach's conjecture, and requires more advanced mathematical knowledge.
Author: Krishnaswami Alladi Publisher: Springer Science & Business Media ISBN: 1441962638 Category : Mathematics Languages : en Pages : 571
Book Description
In the spirit of Alladi Ramakrishnan’s profound interest and contributions to three fields of science — Mathematics, Statistics, and Physics — this volume contains invited surveys and research articles from prominent members of these communities who also knew Ramakrishnan personally and greatly respected his influence in these areas of science. Historical photos, telegrams, and biographical narratives of Alladi Ramakrishnan’s illustrious career of special interest are included as well.
Author: Vadim Gorin Publisher: Cambridge University Press ISBN: 1108922902 Category : Mathematics Languages : en Pages : 262
Book Description
Over the past 25 years, there has been an explosion of interest in the area of random tilings. The first book devoted to the topic, this timely text describes the mathematical theory of tilings. It starts from the most basic questions (which planar domains are tileable?), before discussing advanced topics about the local structure of very large random tessellations. The author explains each feature of random tilings of large domains, discussing several different points of view and leading on to open problems in the field. The book is based on upper-division courses taught to a variety of students but it also serves as a self-contained introduction to the subject. Test your understanding with the exercises provided and discover connections to a wide variety of research areas in mathematics, theoretical physics, and computer science, such as conformal invariance, determinantal point processes, Gibbs measures, high-dimensional random sampling, symmetric functions, and variational problems.
Author: Shaun Cooper Publisher: World Scientific ISBN: 9814366463 Category : Mathematics Languages : en Pages : 185
Book Description
This unique book provides an innovative and efficient approach to elliptic functions, based on the ideas of the great Indian mathematician Srinivasa Ramanujan. The original 1988 monograph of K Venkatachaliengar has been completely revised. Many details, omitted from the original version, have been included, and the book has been made comprehensive by notes at the end of each chapter. The book is for graduate students and researchers in Number Theory and Classical Analysis, as well for scholars and aficionados of Ramanujan''s work. It can be read by anyone with some undergraduate knowledge of real and complex analysis.
Author: Dominique Foata
Author: Dominique Foata
Author: V. Sidoravicius
Author: Alain Lascoux
Author: Bernhard Krötz
Author: Jonathan Borwein
Author: Ranjan Roy
Author: Ranjan Roy
Author: Krishnaswami Alladi
Author: Vadim Gorin
Author: Shaun Cooper