Riordan Arrays: A Primer

Riordan Arrays: A Primer PDF

Author: Paul Barry

Publisher: Lulu.com

Published: 2017-01-09

Total Pages: 310

ISBN-13: 1326855239

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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.

The Riordan Group and Applications

The Riordan Group and Applications PDF

Author: Louis Shapiro

Publisher: Springer Nature

Published: 2022-04-28

Total Pages: 376

ISBN-13: 3030941515

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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.

Combinatorics, Graph Theory and Computing

Combinatorics, Graph Theory and Computing PDF

Author: Frederick Hoffman

Publisher: Springer Nature

Published: 2022-09-13

Total Pages: 327

ISBN-13: 3031053753

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This proceedings volume gathers selected, revised papers presented at the 51st Southeastern International Conference on Combinatorics, Graph Theory and Computing (SEICCGTC 2020), held at Florida Atlantic University in Boca Raton, USA, on March 9-13, 2020. The SEICCGTC is broadly considered to be a trendsetter for other conferences around the world – many of the ideas and themes first discussed at it have subsequently been explored at other conferences and symposia. The conference has been held annually since 1970, in Baton Rouge, Louisiana and Boca Raton, Florida. Over the years, it has grown to become the major annual conference in its fields, and plays a major role in disseminating results and in fostering collaborative work. This volume is intended for the community of pure and applied mathematicians, in academia, industry and government, working in combinatorics and graph theory, as well as related areas of computer science and the interactions among these fields.

Methods for the Summation of Series

Methods for the Summation of Series PDF

Author: Tian-Xiao He

Publisher: CRC Press

Published: 2022-01-26

Total Pages: 458

ISBN-13: 1000534332

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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.

Combinatorics and Number Theory of Counting Sequences

Combinatorics and Number Theory of Counting Sequences PDF

Author: Istvan Mezo

Publisher: CRC Press

Published: 2019-08-19

Total Pages: 480

ISBN-13: 1351346385

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Combinatorics and Number Theory of Counting Sequences is an introduction to the theory of finite set partitions and to the enumeration of cycle decompositions of permutations. The presentation prioritizes elementary enumerative proofs. Therefore, parts of the book are designed so that even those high school students and teachers who are interested in combinatorics can have the benefit of them. Still, the book collects vast, up-to-date information for many counting sequences (especially, related to set partitions and permutations), so it is a must-have piece for those mathematicians who do research on enumerative combinatorics. In addition, the book contains number theoretical results on counting sequences of set partitions and permutations, so number theorists who would like to see nice applications of their area of interest in combinatorics will enjoy the book, too. Features The Outlook sections at the end of each chapter guide the reader towards topics not covered in the book, and many of the Outlook items point towards new research problems. An extensive bibliography and tables at the end make the book usable as a standard reference. Citations to results which were scattered in the literature now become easy, because huge parts of the book (especially in parts II and III) appear in book form for the first time.

Primer on Multiple Sclerosis

Primer on Multiple Sclerosis PDF

Author: Barbara S. Giesser

Publisher: Oxford University Press

Published: 2016-01-29

Total Pages: 613

ISBN-13: 0199341036

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Primer on Multiple Sclerosis, 2nd Edition is an updated reference manual for the practicing clinician. It covers the range of information needed to treat persons with MS, beginning with basic science and immunopathology, thorough differential diagnosis, symptom management and disease modifying therapies. This essential book also includes material covering new and experimental strategies as well as a review of commonly used complementary and alternative modalities that are used by persons with MS.Multiple Sclerosis (MS) is the most common demyelinating disease of the CNS and the third most common cause of disability among young adults. The complex management issues that are often present in the care of individuals with MS may demand the participation of health care professionals from a variety of disciplines, although the team is usually led by a neurologist. It is therefore essential for the neurologist to have a thorough grounding in the basic science and clinical phenomenology of MS. In this second edition of Primer on Multiple Sclerosis, the latest updates on therapeutics are provided, including new medications that have been FDA- approved since the first edition. Includes new diagnostic criteria, as well as any advances made in current diagnostic techniques, e.g. new imaging metrics. Important new information in the basic sciences and pathophysiology of MS is provided as well as newer epidemiologic studies. Treatment algorithms for common symptoms will be expanded, as well as any new guidelines for switching medications for Disease Modifying treatment "failures". The chapter on alternative and complimentary therapies discusses new research on CCSVI. The chapter on legal issues includes information on the putative effect of the Affordable Health Care Act on access to neurologic care and treatments. Finally, there is expanded discussion of progressive forms of MS both from a basic science and treatment perspective.

Polynomial Sequences

Polynomial Sequences PDF

Author: Francesco Aldo Costabile

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2023-12-18

Total Pages: 526

ISBN-13: 3110757249

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Polynomials are useful mathematical tools. They are simply defined and can be calculated quickly on computer systems. They can be differentiated and integrated easily and can be pieced together to form spline curves. After Weierstrass approximation Theorem, polynomial sequences have acquired considerable importance not only in the various branches of Mathematics, but also in Physics, Chemistry and Engineering disciplines. There is a wide literature on specific polynomial sequences. But there is no literature that attempts a systematic exposition of the main basic methods for the study of a generic polynomial sequence and, at the same time, gives an overview of the main polynomial classes and related applications, at least in numerical analysis. In this book, through an elementary matrix calculus-based approach, an attempt is made to fill this gap by exposing dated and very recent results, both theoretical and applied.

Primer on Multiple Sclerosis

Primer on Multiple Sclerosis PDF

Author: Barbara S. Giesser, MD

Publisher: Oxford University Press

Published: 2010-12-01

Total Pages: 501

ISBN-13: 0199708975

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Primer on Multiple Sclerosis was developed to provide a comprehensive overview of the clinical and basic science aspects of MS. It is designed to be of practical use to clinical neurologists, and addresses all of the major issues that may occur in the management of persons with MS. The reader is provided with the latest information on the science of MS, including immunology, genetics, epidemiology and pathology, as well as a summary of the newest directions in basic science research. Guidelines for diagnosis and appropriate use of diagnostic modalities are presented. All clinical aspects of MS are discussed, including extensive information on aspects that may be more challenging for the neurologist to manage, such as sleep disorders and pain. Disease modifying therapies, including those that are FDA approved, as well as off label and experimental therapies are discussed. Finally, there are chapters on employment and legal issues, as well as an overview of clinical trials and clinical trial outcome measures, which are helpful in reviewing the scientific literature in these areas.

Inside the C++ Object Model

Inside the C++ Object Model PDF

Author: Stanley B. Lippman

Publisher: Addison-Wesley Professional

Published: 1996

Total Pages: 280

ISBN-13: 9780201834543

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There is a lot of misinformation and myth about the overhead and costs associated with C++. Now Stan Lippman, the acclaimed author of the C++ Primer, answers the call for a book that gives strategy guidelines for C++ programming. Inside the C++ Object Model explains where overhead costs reside and what they actually consist of. The author explains which parts vary by implementation and which are invariant. He tells how the various implementation models arose, points out areas where they are likely to evolve, and explains why they are what they are. This book is a must for C++ programmers who want to understand the semantic implications of the C++ object model and how the model affects their programs.

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