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Author: Louis Shapiro
Publisher: Springer Nature
ISBN: 3030941515
Category : Mathematics
Languages : en
Pages : 376
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Book Description
The ever-growing applications and richness of approaches to the Riordan group is captured in this comprehensive monograph, authored by those who are among the founders and foremost world experts in this field. The concept of a Riordan array has played a unifying role in enumerative combinatorics over the last three decades. The Riordan arrays and Riordan group is a new growth point in mathematics that is both being influenced by, and continuing its contributions to, other fields such as Lie groups, elliptic curves, orthogonal polynomials, spline functions, networks, sequences and series, Beal conjecture, Riemann hypothesis, to name several. In recent years the Riordan group has made links to quantum field theory and has become a useful tool for computer science and computational chemistry. We can look forward to discovering further applications to unexpected areas of research. Providing a baseline and springboard to further developments and study, this book may also serve as a text for anyone interested in discrete mathematics, including combinatorics, number theory, matrix theory, graph theory, and algebra.
Author: Louis Shapiro
Publisher: Springer Nature
ISBN: 3030941515
Category : Mathematics
Languages : en
Pages : 376
Get Book Here
Book Description
The ever-growing applications and richness of approaches to the Riordan group is captured in this comprehensive monograph, authored by those who are among the founders and foremost world experts in this field. The concept of a Riordan array has played a unifying role in enumerative combinatorics over the last three decades. The Riordan arrays and Riordan group is a new growth point in mathematics that is both being influenced by, and continuing its contributions to, other fields such as Lie groups, elliptic curves, orthogonal polynomials, spline functions, networks, sequences and series, Beal conjecture, Riemann hypothesis, to name several. In recent years the Riordan group has made links to quantum field theory and has become a useful tool for computer science and computational chemistry. We can look forward to discovering further applications to unexpected areas of research. Providing a baseline and springboard to further developments and study, this book may also serve as a text for anyone interested in discrete mathematics, including combinatorics, number theory, matrix theory, graph theory, and algebra.
Author: Tian-Xiao He
Publisher: CRC Press
ISBN: 1000534375
Category : Mathematics
Languages : en
Pages : 301
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Book Description
This book presents methods for the summation of infinite and finite series and the related identities and inversion relations. The summation includes the column sums and row sums of lower triangular matrices. The convergence of the summation of infinite series is considered. The author’s focus is on symbolic methods and the Riordan array approach. In addition, this book contains hundreds summation formulas and identities, which can be used as a handbook for people working in computer science, applied mathematics, and computational mathematics, particularly, combinatorics, computational discrete mathematics, and computational number theory. The exercises at the end of each chapter help deepen understanding. Much of the materials in this book has never appeared before in textbook form. This book can be used as a suitable textbook for advanced courses for high lever undergraduate and lower lever graduate students. It is also an introductory self-study book for re- searchers interested in this field, while some materials of the book can be used as a portal for further research.
Author: Paul Barry
Publisher: Lulu.com
ISBN: 1326855239
Category : Science
Languages : en
Pages : 310
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Book Description
The aim of this text is to introduce the beginner to the theory of Riordan arrays. Starting in a simple and constructive manner, the basic structure of these arrays is explained with clear examples, before a more theoretical grounding is provided. Ordinary Riordan arrays and exponential Riordan arrays are examined, with many explicit examples, and their applications to combinatorics and other areas are explored. The production matrix of a Riordan array is shown to play a key role, along with various sequence characterizations. Formal prerequisites are kept to a minimum, in order to provide a gentle introduction to this exciting area, that involves linear algebra, group theory and combinatorics. The reader will be well positioned to further explore Riordan arrays and their applications, and to undertake their own projects. They will join a community of interested mathematicians that now spans all continents, in a growing area of research and application.
Author: Xiao-Xiong Gan
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110598604
Category : Mathematics
Languages : en
Pages : 297
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Book Description
Formal analysis is the study of formal power series, formal Laurent series, formal root series, and other formal series or formal functionals. This book is the first comprehensive presentation of the topic that systematically introduces formal analysis, including its algebraic, analytic, and topological structure, along with various applications.
Author:
Publisher: ScholarlyEditions
ISBN: 1490105824
Category : Mathematics
Languages : en
Pages : 700
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Book Description
Issues in Algebra, Geometry, and Topology / 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Topology. The editors have built Issues in Algebra, Geometry, and Topology: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Topology in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Algebra, Geometry, and Topology: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Author: Robin Pemantle
Publisher: Cambridge University Press
ISBN: 1107031575
Category : Mathematics
Languages : en
Pages : 395
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Book Description
Aimed at graduate students and researchers in enumerative combinatorics, this book is the first to treat the analytic aspects of combinatorial enumeration from a multivariate perspective.
Author: Nathaniel Dean
Publisher: American Mathematical Soc.
ISBN: 0821811959
Category : Biography & Autobiography
Languages : en
Pages : 184
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Book Description
This volume presents the proceedings of the Fourth Conference for African-American Researchers in the Mathematical Sciences held at the Center for Research on Parallel Computation at Rice University (Houston). The included talks and poster presentations offer a broad perspective to the critical issues involving minority participation in mathematics. The issues explored are relevant not only to African American researchers, but also to the mathematical community in general. This volume is the second published by the AMS (see DIMACS series, volume 15) presenting expository and research papers by distinguished African American mathematicians. In addition to filling the existing gap on African American contributions to mathematics, this book provides leadership direction and role models for students.
Author: Raj Chandra Bose
Publisher:
ISBN:
Category : Combinatorial analysis
Languages : en
Pages : 632
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Book Description
Author: Tian-Xiao He
Publisher: CRC Press
ISBN: 1000534332
Category : Mathematics
Languages : en
Pages : 458
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Book Description
This book presents methods for the summation of infinite and finite series and the related identities and inversion relations. The summation includes the column sums and row sums of lower triangular matrices. The convergence of the summation of infinite series is considered. The author’s focus is on symbolic methods and the Riordan array approach. In addition, this book contains hundreds summation formulas and identities, which can be used as a handbook for people working in computer science, applied mathematics, and computational mathematics, particularly, combinatorics, computational discrete mathematics, and computational number theory. The exercises at the end of each chapter help deepen understanding. Much of the materials in this book has never appeared before in textbook form. This book can be used as a suitable textbook for advanced courses for high lever undergraduate and lower lever graduate students. It is also an introductory self-study book for re- searchers interested in this field, while some materials of the book can be used as a portal for further research.
Author: Victor Kac
Publisher: Springer Science & Business Media
ISBN: 1461300711
Category : Mathematics
Languages : en
Pages : 121
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Book Description
Simply put, quantum calculus is ordinary calculus without taking limits. This undergraduate text develops two types of quantum calculi, the q-calculus and the h-calculus. As this book develops quantum calculus along the lines of traditional calculus, the reader discovers, with a remarkable inevitability, many important notions and results of classical mathematics. This book is written at the level of a first course in calculus and linear algebra and is aimed at undergraduate and beginning graduate students in mathematics, computer science, and physics. It is based on lectures and seminars given by MIT Professor Kac over the last few years at MIT.
