Stirling Numbers

Download Stirling Numbers full books in PDF, epub, and Kindle. Read online Stirling Numbers ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Combinatorial Identities for Stirling Numbers

Author : Jocelyn Quaintance
Publisher : World Scientific
ISBN 13 : 9814725285
Total Pages : 277 pages
Book Rating : 4.8/5 (147 download)

DOWNLOAD NOW!

Book Synopsis Combinatorial Identities for Stirling Numbers by : Jocelyn Quaintance

Download or read book Combinatorial Identities for Stirling Numbers written by Jocelyn Quaintance and published by World Scientific. This book was released on 2015-10-27 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is a unique work which provides an in-depth exploration into the mathematical expertise, philosophy, and knowledge of H W Gould. It is written in a style that is accessible to the reader with basic mathematical knowledge, and yet contains material that will be of interest to the specialist in enumerative combinatorics. This book begins with exposition on the combinatorial and algebraic techniques that Professor Gould uses for proving binomial identities. These techniques are then applied to develop formulas which relate Stirling numbers of the second kind to Stirling numbers of the first kind. Professor Gould's techniques also provide connections between both types of Stirling numbers and Bernoulli numbers. Professor Gould believes his research success comes from his intuition on how to discover combinatorial identities. This book will appeal to a wide audience and may be used either as lecture notes for a beginning graduate level combinatorics class, or as a research supplement for the specialist in enumerative combinatorics."--

Stirling Numbers

Author : Elena Deza
Publisher : World Scientific
ISBN 13 : 9811278113
Total Pages : 467 pages
Book Rating : 4.8/5 (112 download)

DOWNLOAD NOW!

Book Synopsis Stirling Numbers by : Elena Deza

Download or read book Stirling Numbers written by Elena Deza and published by World Scientific. This book was released on 2023-12-27 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stirling numbers are one of the most known classes of special numbers in Mathematics, especially in Combinatorics and Algebra. They were introduced by Scottish mathematician James Stirling (1692-1770) in his most important work, Differential Method with a Tract on Summation and Interpolation of Infinite Series (1730). Stirling numbers have a rich history; many arithmetic, number-theoretical, analytical and combinatorial connections; numerous classical properties; as well as many modern applications.This book collects much of the scattered material on the two subclasses of Stirling numbers to provide a holistic overview of the topic. From the combinatorial point of view, Stirling numbers of the second kind, S(n, k), count the number of ways to partition a set of n different objects (i.e., a given n-set) into k non-empty subsets. Stirling numbers of the first kind, s(n, k), give the number of permutations of n elements with k disjoint cycles. Both subclasses of Stirling numbers play an important role in Algebra: they form the coefficients, connecting well-known sets of polynomials.This book is suitable for students and professionals, providing a broad perspective of the theory of this class of special numbers, and many generalisations and relatives of Stirling numbers, including Bell numbers and Lah numbers. Throughout the book, readers are provided exercises to test and cement their understanding.

Commutation Relations, Normal Ordering, and Stirling Numbers

Author : Toufik Mansour
Publisher : CRC Press
ISBN 13 : 1466579897
Total Pages : 506 pages
Book Rating : 4.4/5 (665 download)

DOWNLOAD NOW!

Book Synopsis Commutation Relations, Normal Ordering, and Stirling Numbers by : Toufik Mansour

Download or read book Commutation Relations, Normal Ordering, and Stirling Numbers written by Toufik Mansour and published by CRC Press. This book was released on 2015-09-18 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Commutation Relations, Normal Ordering, and Stirling Numbers provides an introduction to the combinatorial aspects of normal ordering in the Weyl algebra and some of its close relatives. The Weyl algebra is the algebra generated by two letters U and V subject to the commutation relation UV - VU = I. It is a classical result that normal ordering pow

Applications of Fibonacci Numbers

Author : G.E. Bergum
Publisher : Springer Science & Business Media
ISBN 13 : 9780792305231
Total Pages : 402 pages
Book Rating : 4.3/5 (52 download)

DOWNLOAD NOW!

Book Synopsis Applications of Fibonacci Numbers by : G.E. Bergum

Download or read book Applications of Fibonacci Numbers written by G.E. Bergum and published by Springer Science & Business Media. This book was released on 1989-12-31 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains thirty-six papers from among the forty-five papers presented at the Third International Conference on Fibonacci Numbers and Their Applications which was held in Pisa, Italy from July 25 to July 29, 1988 in honor of Leonardo de Pisa. These papers have been selected after a careful review by well known referees in the field, and they range from elementary number theory to probability and statistics. The Fibonacci numbers are their unifying bond. It is anticipated that this book, like its two predecessors, will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. August 1989 The Editors Gerald E. Bergum South Dakota State University Brookings, South Dakota, U. S. A. Andreas N. Philippou Ministry of Education Nicosia, Cyprus Alwyn F. Horadam University of New England Armidale N. S. W. , Australia xv THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Dvornicich, Roberto, Chairman Horadam, A. F. (Australia), Co-chairman Filipponi, Piero Philippou, A. N. (Cyprus), Co-chairman Perelli, Alberto Ando, S. (Japan) Viola, Carlo Bergum, G. E. (U. S. A. ) Zannier, Umberto Johnson, M. B. (U. S. A. ) Kiss, P. (Hungary) Tijdeman, Robert (The Netherlands) Tognetti, K. (Australia) XVII LIST OF CONTRIBUTORS TO THE CONFERENCE' ADLER, I. , RR 1, Box 532, North Bennington, VT 05257-9748. "Separating the Biological from the Mathematical Aspects of Phyllotaxis. " *AKRITAS, A. G. , (coauthor P. G. Bradford). "The Role of the Fibonacci Sequence in the Isolation of the Real Roots of Polynomial Equations.

Enumerative Combinatorics

Author : Charalambos A. Charalambides
Publisher : CRC Press
ISBN 13 : 9781584882909
Total Pages : 630 pages
Book Rating : 4.8/5 (829 download)

DOWNLOAD NOW!

Book Synopsis Enumerative Combinatorics by : Charalambos A. Charalambides

Download or read book Enumerative Combinatorics written by Charalambos A. Charalambides and published by CRC Press. This book was released on 2002-05-29 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: Enumerative Combinatorics presents elaborate and systematic coverage of the theory of enumeration. The first seven chapters provide the necessary background, including basic counting principles and techniques, elementary enumerative topics, and an extended presentation of generating functions and recurrence relations. The remaining seven chapters focus on more advanced topics, including, Stirling numbers, partitions of integers, partition polynomials, Eulerian numbers and Polya's counting theorem. Extensively classroom tested, this text was designed for introductory- and intermediate-level courses in enumerative combinatorics, but the far-reaching applications of the subject also make the book useful to those in operational research, the physical and social science, and anyone who uses combinatorial methods. Remarks, discussions, tables, and numerous examples support the text, and a wealth of exercises-with hints and answers provided in an appendix--further illustrate the subject's concepts, theorems, and applications.

Handbook of Number Theory II

Author : J. Sándor
Publisher : Springer Science & Business Media
ISBN 13 : 1402025467
Total Pages : 637 pages
Book Rating : 4.4/5 (2 download)

DOWNLOAD NOW!

Book Synopsis Handbook of Number Theory II by : J. Sándor

Download or read book Handbook of Number Theory II written by J. Sándor and published by Springer Science & Business Media. This book was released on 2004 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook focuses on some important topics from Number Theory and Discrete Mathematics. These include the sum of divisors function with the many old and new issues on Perfect numbers; Euler's totient and its many facets; the Möbius function along with its generalizations, extensions, and applications; the arithmetic functions related to the divisors or the digits of a number; the Stirling, Bell, Bernoulli, Euler and Eulerian numbers, with connections to various fields of pure or applied mathematics. Each chapter is a survey and can be viewed as an encyclopedia of the considered field, underlining the interconnections of Number Theory with Combinatorics, Numerical mathematics, Algebra, or Probability Theory. This reference work will be useful to specialists in number theory and discrete mathematics as well as mathematicians or scientists who need access to some of these results in other fields of research.

A Walk Through Combinatorics

Author : Mikl¢s B¢na
Publisher : World Scientific
ISBN 13 : 9812568859
Total Pages : 492 pages
Book Rating : 4.8/5 (125 download)

DOWNLOAD NOW!

Book Synopsis A Walk Through Combinatorics by : Mikl¢s B¢na

Download or read book A Walk Through Combinatorics written by Mikl¢s B¢na and published by World Scientific. This book was released on 2006 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. Just as with the first edition, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible for the talented and hard-working undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings and Eulerian and Hamiltonian cycles. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, and algorithms and complexity. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.

Handbook of Mathematical Functions

Author : Milton Abramowitz
Publisher : Courier Corporation
ISBN 13 : 9780486612720
Total Pages : 1068 pages
Book Rating : 4.6/5 (127 download)

DOWNLOAD NOW!

Book Synopsis Handbook of Mathematical Functions by : Milton Abramowitz

Download or read book Handbook of Mathematical Functions written by Milton Abramowitz and published by Courier Corporation. This book was released on 1965-01-01 with total page 1068 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extensive summary of mathematical functions that occur in physical and engineering problems

A Comprehensive Treatment of q-Calculus

Author : Thomas Ernst
Publisher : Springer Science & Business Media
ISBN 13 : 3034804318
Total Pages : 491 pages
Book Rating : 4.0/5 (348 download)

DOWNLOAD NOW!

Book Synopsis A Comprehensive Treatment of q-Calculus by : Thomas Ernst

Download or read book A Comprehensive Treatment of q-Calculus written by Thomas Ernst and published by Springer Science & Business Media. This book was released on 2012-09-13 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: To date, the theoretical development of q-calculus has rested on a non-uniform basis. Generally, the bulky Gasper-Rahman notation was used, but the published works on q-calculus looked different depending on where and by whom they were written. This confusion of tongues not only complicated the theoretical development but also contributed to q-calculus remaining a neglected mathematical field. This book overcomes these problems by introducing a new and interesting notation for q-calculus based on logarithms.For instance, q-hypergeometric functions are now visually clear and easy to trace back to their hypergeometric parents. With this new notation it is also easy to see the connection between q-hypergeometric functions and the q-gamma function, something that until now has been overlooked. The book covers many topics on q-calculus, including special functions, combinatorics, and q-difference equations. Apart from a thorough review of the historical development of q-calculus, this book also presents the domains of modern physics for which q-calculus is applicable, such as particle physics and supersymmetry, to name just a few.

The American Mathematical Monthly

Author :
Publisher :
ISBN 13 :
Total Pages : 614 pages
Book Rating : 4.3/5 (91 download)

DOWNLOAD NOW!

Book Synopsis The American Mathematical Monthly by :

Download or read book The American Mathematical Monthly written by and published by . This book was released on 1928 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes section "Recent publications."

Introduction to Combinatorics

Author : Martin J. Erickson
Publisher : John Wiley & Sons
ISBN 13 : 1118030893
Total Pages : 210 pages
Book Rating : 4.1/5 (18 download)

DOWNLOAD NOW!

Book Synopsis Introduction to Combinatorics by : Martin J. Erickson

Download or read book Introduction to Combinatorics written by Martin J. Erickson and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This gradual, systematic introduction to the main concepts of combinatorics is the ideal text for advanced undergraduate and early graduate courses in this subject. Each of the book's three sections--Existence, Enumeration, and Construction--begins with a simply stated first principle, which is then developed step by step until it leads to one of the three major achievements of combinatorics: Van der Waerden's theorem on arithmetic progressions, Polya's graph enumeration formula, and Leech's 24-dimensional lattice. Along the way, Professor Martin J. Erickson introduces fundamental results, discusses interconnection and problem-solving techniques, and collects and disseminates open problems that raise new and innovative questions and observations. His carefully chosen end-of-chapter exercises demonstrate the applicability of combinatorial methods to a wide variety of problems, including many drawn from the William Lowell Putnam Mathematical Competition. Many important combinatorial methods are revisited several times in the course of the text--in exercises and examples as well as theorems and proofs. This repetition enables students to build confidence and reinforce their understanding of complex material. Mathematicians, statisticians, and computer scientists profit greatly from a solid foundation in combinatorics. Introduction to Combinatorics builds that foundation in an orderly, methodical, and highly accessible manner.

James Stirling’s Methodus Differentialis

Author : Ian Tweddle
Publisher : Springer Science & Business Media
ISBN 13 : 1447100212
Total Pages : 301 pages
Book Rating : 4.4/5 (471 download)

DOWNLOAD NOW!

Book Synopsis James Stirling’s Methodus Differentialis by : Ian Tweddle

Download or read book James Stirling’s Methodus Differentialis written by Ian Tweddle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new translation makes this classic and important text more generally accessible. The text is placed in its contemporary context, but also related to the interests of practising mathematicians today. This book will be of interest to mathematical historians, researchers, and numerical analysts.

Introduction to Combinatorics

Author : Walter D. Wallis
Publisher : CRC Press
ISBN 13 : 1498777627
Total Pages : 364 pages
Book Rating : 4.4/5 (987 download)

DOWNLOAD NOW!

Book Synopsis Introduction to Combinatorics by : Walter D. Wallis

Download or read book Introduction to Combinatorics written by Walter D. Wallis and published by CRC Press. This book was released on 2016-12-12 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: What Is Combinatorics Anyway? Broadly speaking, combinatorics is the branch of mathematics dealing with different ways of selecting objects from a set or arranging objects. It tries to answer two major kinds of questions, namely, counting questions: how many ways can a selection or arrangement be chosen with a particular set of properties; and structural questions: does there exist a selection or arrangement of objects with a particular set of properties? The authors have presented a text for students at all levels of preparation. For some, this will be the first course where the students see several real proofs. Others will have a good background in linear algebra, will have completed the calculus stream, and will have started abstract algebra. The text starts by briefly discussing several examples of typical combinatorial problems to give the reader a better idea of what the subject covers. The next chapters explore enumerative ideas and also probability. It then moves on to enumerative functions and the relations between them, and generating functions and recurrences., Important families of functions, or numbers and then theorems are presented. Brief introductions to computer algebra and group theory come next. Structures of particular interest in combinatorics: posets, graphs, codes, Latin squares, and experimental designs follow. The authors conclude with further discussion of the interaction between linear algebra and combinatorics. Features Two new chapters on probability and posets. Numerous new illustrations, exercises, and problems. More examples on current technology use A thorough focus on accuracy Three appendices: sets, induction and proof techniques, vectors and matrices, and biographies with historical notes, Flexible use of MapleTM and MathematicaTM

Combinatorics

Author : Nicholas Loehr
Publisher : CRC Press
ISBN 13 : 1498780261
Total Pages : 618 pages
Book Rating : 4.4/5 (987 download)

DOWNLOAD NOW!

Book Synopsis Combinatorics by : Nicholas Loehr

Download or read book Combinatorics written by Nicholas Loehr and published by CRC Press. This book was released on 2017-08-10 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics, Second Edition is a well-rounded, general introduction to the subjects of enumerative, bijective, and algebraic combinatorics. The textbook emphasizes bijective proofs, which provide elegant solutions to counting problems by setting up one-to-one correspondences between two sets of combinatorial objects. The author has written the textbook to be accessible to readers without any prior background in abstract algebra or combinatorics. Part I of the second edition develops an array of mathematical tools to solve counting problems: basic counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear algebraic methods. These tools are used to analyze combinatorial structures such as words, permutations, subsets, functions, graphs, trees, lattice paths, and much more. Part II cover topics in algebraic combinatorics including group actions, permutation statistics, symmetric functions, and tableau combinatorics. This edition provides greater coverage of the use of ordinary and exponential generating functions as a problem-solving tool. Along with two new chapters, several new sections, and improved exposition throughout, the textbook is brimming with many examples and exercises of various levels of difficulty.

Patterns in Permutations and Words

Author : Sergey Kitaev
Publisher : Springer Science & Business Media
ISBN 13 : 3642173330
Total Pages : 511 pages
Book Rating : 4.6/5 (421 download)

DOWNLOAD NOW!

Book Synopsis Patterns in Permutations and Words by : Sergey Kitaev

Download or read book Patterns in Permutations and Words written by Sergey Kitaev and published by Springer Science & Business Media. This book was released on 2011-08-30 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has been considerable interest recently in the subject of patterns in permutations and words, a new branch of combinatorics with its roots in the works of Rotem, Rogers, and Knuth in the 1970s. Consideration of the patterns in question has been extremely interesting from the combinatorial point of view, and it has proved to be a useful language in a variety of seemingly unrelated problems, including the theory of Kazhdan—Lusztig polynomials, singularities of Schubert varieties, interval orders, Chebyshev polynomials, models in statistical mechanics, and various sorting algorithms, including sorting stacks and sortable permutations. The author collects the main results in the field in this up-to-date, comprehensive reference volume. He highlights significant achievements in the area, and points to research directions and open problems. The book will be of interest to researchers and graduate students in theoretical computer science and mathematics, in particular those working in algebraic combinatorics and combinatorics on words. It will also be of interest to specialists in other branches of mathematics, theoretical physics, and computational biology. The author collects the main results in the field in this up-to-date, comprehensive reference volume. He highlights significant achievements in the area, and points to research directions and open problems. The book will be of interest to researchers and graduate students in theoretical computer science and mathematics, in particular those working in algebraic combinatorics and combinatorics on words. It will also be of interest to specialists in other branches of mathematics, theoretical physics, and computational biology.

7 Algorithm Design Paradigms

Author : Sung-Hyuk Cha
Publisher : Cha Academy llc
ISBN 13 : 1735168009
Total Pages : 798 pages
Book Rating : 4.7/5 (351 download)

DOWNLOAD NOW!

Book Synopsis 7 Algorithm Design Paradigms by : Sung-Hyuk Cha

Download or read book 7 Algorithm Design Paradigms written by Sung-Hyuk Cha and published by Cha Academy llc. This book was released on 2020-06-01 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: The intended readership includes both undergraduate and graduate students majoring in computer science as well as researchers in the computer science area. The book is suitable either as a textbook or as a supplementary book in algorithm courses. Over 400 computational problems are covered with various algorithms to tackle them. Rather than providing students simply with the best known algorithm for a problem, this book presents various algorithms for readers to master various algorithm design paradigms. Beginners in computer science can train their algorithm design skills via trivial algorithms on elementary problem examples. Graduate students can test their abilities to apply the algorithm design paradigms to devise an efficient algorithm for intermediate-level or challenging problems. Key Features: Dictionary of computational problems: A table of over 400 computational problems with more than 1500 algorithms is provided. Indices and Hyperlinks: Algorithms, computational problems, equations, figures, lemmas, properties, tables, and theorems are indexed with unique identification numbers and page numbers in the printed book and hyperlinked in the e-book version. Extensive Figures: Over 435 figures illustrate the algorithms and describe computational problems. Comprehensive exercises: More than 352 exercises help students to improve their algorithm design and analysis skills. The answers for most questions are available in the accompanying solution manual.

Handbook of Mathematics

Author : Thierry Vialar
Publisher : BoD - Books on Demand
ISBN 13 : 2955199044
Total Pages : 1134 pages
Book Rating : 4.9/5 (551 download)

DOWNLOAD NOW!

Book Synopsis Handbook of Mathematics by : Thierry Vialar

Download or read book Handbook of Mathematics written by Thierry Vialar and published by BoD - Books on Demand. This book was released on 2016-12-07 with total page 1134 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book, revised, consists of XI Parts and 28 Chapters covering all areas of mathematics. It is a tool for students, scientists, engineers, students of many disciplines, teachers, professionals, writers and also for a general reader with an interest in mathematics and in science. It provides a wide range of mathematical concepts, definitions, propositions, theorems, proofs, examples, and numerous illustrations. The difficulty level can vary depending on chapters, and sustained attention will be required for some. The structure and list of Parts are quite classical: I. Foundations of Mathematics, II. Algebra, III. Number Theory, IV. Geometry, V. Analytic Geometry, VI. Topology, VII. Algebraic Topology, VIII. Analysis, IX. Category Theory, X. Probability and Statistics, XI. Applied Mathematics. Appendices provide useful lists of symbols and tables for ready reference. Extensive cross-references allow readers to find related terms, concepts and items (by page number, heading, and objet such as theorem, definition, example, etc.). The publisher’s hope is that this book, slightly revised and in a convenient format, will serve the needs of readers, be it for study, teaching, exploration, work, or research.