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The Riordan Group and Applications

2022-04-28 Mathematics
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Release : 2022-04-28
Genre : Mathematics
Kind : eBook
Book Rating : 515/5 ( reviews)

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Book Synopsis The Riordan Group and Applications by : Louis Shapiro

Download or read book The Riordan Group and Applications written by Louis Shapiro. This book was released on 2022-04-28. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Riordan Arrays: A Primer

2017-01-09 Combinatorial analysis
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Release : 2017-01-09
Genre : Combinatorial analysis
Kind : eBook
Book Rating : 239/5 ( reviews)

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Book Synopsis Riordan Arrays: A Primer by : Paul Barry

Download or read book Riordan Arrays: A Primer written by Paul Barry. This book was released on 2017-01-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

African Americans in Mathematics II

1999 Biography & Autobiography
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Release : 1999
Genre : Biography & Autobiography
Kind : eBook
Book Rating : 959/5 ( reviews)

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Book Synopsis African Americans in Mathematics II by : Nathaniel Dean

Download or read book African Americans in Mathematics II written by Nathaniel Dean. This book was released on 1999. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Methods for the Summation of Series

2022-01-26 Mathematics
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Release : 2022-01-26
Genre : Mathematics
Kind : eBook
Book Rating : 332/5 ( reviews)

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Book Synopsis Methods for the Summation of Series by : Tian-Xiao He

Download or read book Methods for the Summation of Series written by Tian-Xiao He. This book was released on 2022-01-26. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Formal Analysis

2021-06-08 Mathematics
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Release : 2021-06-08
Genre : Mathematics
Kind : eBook
Book Rating : 604/5 ( reviews)

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Book Synopsis Formal Analysis by : Xiao-Xiong Gan

Download or read book Formal Analysis written by Xiao-Xiong Gan. This book was released on 2021-06-08. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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