Combinatorial Identities For Stirling Numbers

Author : Jocelyn Quaintance
Publisher : World Scientific
ISBN 13 : 9814725285
Total Pages : 277 pages
Book Rating : 4.86/5 ( download)

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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."--

Author : Arthur T. Benjamin
Publisher : American Mathematical Society
ISBN 13 : 1470472597
Total Pages : 210 pages
Book Rating : 4.97/5 ( download)

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Download or read book Proofs that Really Count written by Arthur T. Benjamin and published by American Mathematical Society. This book was released on 2022-09-21 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. In Proofs That Really Count, award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguments. The book emphasizes numbers that are often not thought of as numbers that count: Fibonacci Numbers, Lucas Numbers, Continued Fractions, and Harmonic Numbers, to name a few. Numerous hints and references are given for all chapter exercises and many chapters end with a list of identities in need of combinatorial proof. The extensive appendix of identities will be a valuable resource. This book should appeal to readers of all levels, from high school math students to professional mathematicians.

Author : Louis Comtet
Publisher : Springer Science & Business Media
ISBN 13 : 9401021961
Total Pages : 353 pages
Book Rating : 4.68/5 ( download)

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Download or read book Advanced Combinatorics written by Louis Comtet and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Notwithstanding its title, the reader will not find in this book a systematic account of this huge subject. Certain classical aspects have been passed by, and the true title ought to be "Various questions of elementary combina torial analysis". For instance, we only touch upon the subject of graphs and configurations, but there exists a very extensive and good literature on this subject. For this we refer the reader to the bibliography at the end of the volume. The true beginnings of combinatorial analysis (also called combina tory analysis) coincide with the beginnings of probability theory in the 17th century. For about two centuries it vanished as an autonomous sub ject. But the advance of statistics, with an ever-increasing demand for configurations as well as the advent and development of computers, have, beyond doubt, contributed to reinstating this subject after such a long period of negligence. For a long time the aim of combinatorial analysis was to count the different ways of arranging objects under given circumstances. Hence, many of the traditional problems of analysis or geometry which are con cerned at a certain moment with finite structures, have a combinatorial character. Today, combinatorial analysis is also relevant to problems of existence, estimation and structuration, like all other parts of mathema tics, but exclusively forjinite sets.

Author : Boyadzhiev Khristo N
Publisher : World Scientific
ISBN 13 : 9813234997
Total Pages : 208 pages
Book Rating : 4.94/5 ( download)

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Download or read book Notes On The Binomial Transform: Theory And Table With Appendix On Stirling Transform written by Boyadzhiev Khristo N and published by World Scientific. This book was released on 2018-04-10 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The binomial transform is a discrete transformation of one sequence into another with many interesting applications in combinatorics and analysis. This volume is helpful to researchers interested in enumerative combinatorics, special numbers, and classical analysis. A valuable reference, it can also be used as lecture notes for a course in binomial identities, binomial transforms and Euler series transformations. The binomial transform leads to various combinatorial and analytical identities involving binomial coefficients. In particular, we present here new binomial identities for Bernoulli, Fibonacci, and harmonic numbers. Many interesting identities can be written as binomial transforms and vice versa. The volume consists of two parts. In the first part, we present the theory of the binomial transform for sequences with a sufficient prerequisite of classical numbers and polynomials. The first part provides theorems and tools which help to compute binomial transforms of different sequences and also to generate new binomial identities from the old. These theoretical tools (formulas and theorems) can also be used for summation of series and various numerical computations. In the second part, we have compiled a list of binomial transform formulas for easy reference. In the Appendix, we present the definition of the Stirling sequence transform and a short table of transformation formulas. Contents: Theory of the Binomial Transform: Introduction Prerequisite: Special Numbers and Polynomials Euler's Transformation for Series Melzak's Formula and Related Formulas Special Properties. Creating New Identities Binomial Transforms of Products Special Formulas and Power Series with Binomial Sums Table of Binomial Transforms: Assorted Binomial Formulas Identities Involving Harmonic Numbers Transforms of Binomial Coefficients Transforms of Special Numbers and Polynomials Transforms of Trigonometric and Hyperbolic Functions and Applications to Some Trigonometric Integrals Transforms of Some Special Functions Appendix: The Stirling Transform of Sequences Readership: Graduate and researchers in the areas of number theory, discrete mathematics, combinatorics, statistics working with applications using the binomial transform. Keywords: Binomial Coefficients;Binomial Identities;Binomial Sums;Binomial Transform;Euler's Series Transformation;Discrete Mathematics;Finite Differences;Stirling Numbers of the First Kind;Stirling Numbers of the Second Kind;Stirling Transform;Special Numbers and Polynomials;Harmonic Numbers;Bernoulli Numbers;Fibonacci Numbers;Melzak's Formula;Exponential Polynomials;Geometric Polynomials;Laguerre Polynomials;Trigonometric IntegralsReview: Key Features: This is the first, long-overdue book on the subject. (At present, there are no competing books) The book provides interesting new material for researchers in discrete mathematics and will serve as a valuable reference for binomial identities, binomial transform formulas, and Euler series transformations

Author : John Riordan
Publisher :
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.68/5 ( download)

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Download or read book Combinatorial Identities written by John Riordan and published by . This book was released on 1979 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Michael Z. Spivey
Publisher : CRC Press
ISBN 13 : 1351215809
Total Pages : 231 pages
Book Rating : 4.00/5 ( download)

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Download or read book The Art of Proving Binomial Identities written by Michael Z. Spivey and published by CRC Press. This book was released on 2019-05-10 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book has two goals: (1) Provide a unified treatment of the binomial coefficients, and (2) Bring together much of the undergraduate mathematics curriculum via one theme (the binomial coefficients). The binomial coefficients arise in a variety of areas of mathematics: combinatorics, of course, but also basic algebra (binomial theorem), infinite series (Newton’s binomial series), differentiation (Leibniz’s generalized product rule), special functions (the beta and gamma functions), probability, statistics, number theory, finite difference calculus, algorithm analysis, and even statistical mechanics.

Author : Bruce E. Sagan
Publisher : American Mathematical Soc.
ISBN 13 : 1470460327
Total Pages : 304 pages
Book Rating : 4.27/5 ( download)

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Download or read book Combinatorics: The Art of Counting written by Bruce E. Sagan and published by American Mathematical Soc.. This book was released on 2020-10-16 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance. The book assumes minimal background, and a first course in abstract algebra should suffice. The exposition is very reader friendly: keeping a moderate pace, using lots of examples, emphasizing recurring themes, and frankly expressing the delight the author takes in mathematics in general and combinatorics in particular.

Author : Philippe Flajolet
Publisher : Cambridge University Press
ISBN 13 : 1139477161
Total Pages : 825 pages
Book Rating : 4.61/5 ( download)

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Download or read book Analytic Combinatorics written by Philippe Flajolet and published by Cambridge University Press. This book was released on 2009-01-15 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.

Author : Johannes Blömer
Publisher : Springer
ISBN 13 : 3319724533
Total Pages : 462 pages
Book Rating : 4.39/5 ( download)

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Download or read book Mathematical Aspects of Computer and Information Sciences written by Johannes Blömer and published by Springer. This book was released on 2017-12-20 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 7th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2017, held in Vienna, Austria, in November 2017. The 28 revised papers and 8 short papers presented were carefully reviewed and selected from 67 submissions. The papers are organized in the following topical sections: foundation of algorithms in mathematics, engineering and scientific computation; combinatorics and codes in computer science; data modeling and analysis; and mathematical aspects of information security and cryptography.

Author : Ian Tweddle
Publisher : Springer Science & Business Media
ISBN 13 : 1447100212
Total Pages : 301 pages
Book Rating : 4.18/5 ( download)

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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.