Stirling Polynomials In Several Indeterminates
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Stirling Polynomials In Several Indeterminates
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Author : Alfred Schreiber
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2021
Stirling Polynomials In Several Indeterminates written by Alfred Schreiber and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Mathematics categories.
The classical exponential polynomials, today commonly named after E.,T. Bell, have a wide range of remarkable applications in Combinatorics, Algebra, Analysis, and Mathematical Physics. Within the algebraic framework presented in this book they appear as structural coefficients in finite expansions of certain higher-order derivative operators. In this way, a correspondence between polynomials and functions is established, which leads (via compositional inversion) to the specification and the effective computation of orthogonal companions of the Bell polynomials. Together with the latter, one obtains the larger class of multivariate `Stirling polynomials'. Their fundamental recurrences and inverse relations are examined in detail and shown to be directly related to corresponding identities for the Stirling numbers. The following topics are also covered: polynomial families that can be represented by Bell polynomials; inversion formulas, in particular of Schlömilch-Schläfli type; applications to binomial sequences; new aspects of the Lagrange inversion, and, as a highlight, reciprocity laws, which unite a polynomial family and that of orthogonal companions. Besides a Mathematica(R) package and an extensive bibliography, additional material is compiled in a number of notes and supplements.
Stirling Polynomials In Several Indeterminates
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Author : Alfred Schreiber
language : en
Publisher:
Release Date : 2021
Stirling Polynomials In Several Indeterminates written by Alfred Schreiber and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Electronic books categories.
Commutation Relations Normal Ordering And Stirling Numbers
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Author : Toufik Mansour
language : en
Publisher: CRC Press
Release Date : 2015-09-18
Commutation Relations Normal Ordering And Stirling Numbers written by Toufik Mansour and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-18 with Mathematics categories.
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
Certain Number Theoretic Episodes In Algebra
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Author : Sivaramakrishnan R
language : en
Publisher: CRC Press
Release Date : 2006-09-22
Certain Number Theoretic Episodes In Algebra written by Sivaramakrishnan R and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-22 with Mathematics categories.
Many basic ideas of algebra and number theory intertwine, making it ideal to explore both at the same time. Certain Number-Theoretic Episodes in Algebra focuses on some important aspects of interconnections between number theory and commutative algebra. Using a pedagogical approach, the author presents the conceptual foundations of commutati
Die Entt Uschte Erkenntnis
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Author : Alfred Schreiber
language : de
Publisher: Logos Verlag Berlin GmbH
Release Date : 2022-08-08
Die Entt Uschte Erkenntnis written by Alfred Schreiber and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-08 with Mathematics categories.
Drei Dutzend Essays laden zu unterhaltsamen Streifzügen im Umfeld der Mathematik ein. Zur Sprache kommen denk- und fragwürdige Innen- und Außenansichten des Fachs: Facetten, die sich mit Kultur und Künsten, Literatur und Dichtung, Ideengeschichte und Gesellschaft berühren - gar nicht selten an Reibungsflächen. Die lockere, bisweilen kritisch-satirische Sicht- und Schreibweise des Autors bringt das Fesselnde und wunderbar Denkanstößige zum Vorschein, das die Rolle der Mathematik in Alltag, Kultur und Wissenschaft immer wieder zeitigt. Ein großer Teil der Texte beruht auf einer Kolumne, die zwischen 2002 und 2012 in den "Mitteilungen der Deutschen Mathematiker-Vereinigung" erschienen ist.
Combinatorics
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Author : David R. Mazur
language : en
Publisher: American Mathematical Society
Release Date : 2022-12-20
Combinatorics written by David R. Mazur and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-20 with Mathematics categories.
Combinatorics is mathematics of enumeration, existence, construction, and optimization questions concerning finite sets. This text focuses on the first three types of questions and covers basic counting and existence principles, distributions, generating functions, recurrence relations, Pólya theory, combinatorial designs, error correcting codes, partially ordered sets, and selected applications to graph theory including the enumeration of trees, the chromatic polynomial, and introductory Ramsey theory. The only prerequisites are single-variable calculus and familiarity with sets and basic proof techniques. The text emphasizes the brands of thinking that are characteristic of combinatorics: bijective and combinatorial proofs, recursive analysis, and counting problem classification. It is flexible enough to be used for undergraduate courses in combinatorics, second courses in discrete mathematics, introductory graduate courses in applied mathematics programs, as well as for independent study or reading courses. What makes this text a guided tour are the approximately 350 reading questions spread throughout its eight chapters. These questions provide checkpoints for learning and prepare the reader for the end-of-section exercises of which there are over 470. Most sections conclude with Travel Notes that add color to the material of the section via anecdotes, open problems, suggestions for further reading, and biographical information about mathematicians involved in the discoveries.
Stirling Numbers
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Author : Elena Deza
language : en
Publisher: World Scientific
Release Date : 2023-12-27
Stirling Numbers written by Elena Deza and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-27 with Mathematics categories.
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.
Analytic Combinatorics
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Author : Philippe Flajolet
language : en
Publisher: Cambridge University Press
Release Date : 2009-01-15
Analytic Combinatorics written by Philippe Flajolet and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-15 with Mathematics categories.
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.
Applications And Computation Of Orthogonal Polynomials
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Author : Walter Gautschi
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Applications And Computation Of Orthogonal Polynomials written by Walter Gautschi and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
The workshop on Applications and Computation of Orthogonal Polynomials took place March 22-28, 1998 at the Oberwolfach Mathematical Research Institute. It was the first workshop on this topic ever held at Oberwolfach. There were 46 participants from 13 countries, more than half coming from Germany and the United States, and a substantial number from Italy. A total of 23 plenary lectures were presented and 4 short informal talks. Open problems were discussed during an evening session. This volume contains refereed versions of 18 papers presented at, or submitted to, the conference. The theory of orthogonal polynomials, as a branch of classical analysis, is well established. But orthogonal polynomials play also an important role in many areas of scientific computing, such as least squares fitting, numerical integration, and solving linear algebraic systems. Though the basic tenets have their roots in 19th century mathematics, the use of modern computers has required the development and study of new algorithms that are accurate and robust. The computational methods and applications represented in this volume, of necessity, are incomplete, yet sufficiently varied to convey an impression of current activities in this area.
The Complexity Of Robot Motion Planning
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Author : John Canny
language : en
Publisher: MIT Press
Release Date : 1988
The Complexity Of Robot Motion Planning written by John Canny and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Computers categories.
The Complexity of Robot Motion Planning makes original contributions both to roboticsand to the analysis of algorithms. In this groundbreaking monograph John Canny resolveslong-standing problems concerning the complexity of motion planning and, for the central problem offinding a collision free path for a jointed robot in the presence of obstacles, obtains exponentialspeedups over existing algorithms by applying high-powered new mathematical techniques.Canny's newalgorithm for this "generalized movers' problem," the most-studied and basic robot motion planningproblem, has a single exponential running time, and is polynomial for any given robot. The algorithmhas an optimal running time exponent and is based on the notion of roadmaps - one-dimensionalsubsets of the robot's configuration space. In deriving the single exponential bound, Cannyintroduces and reveals the power of two tools that have not been previously used in geometricalgorithms: the generalized (multivariable) resultant for a system of polynomials and Whitney'snotion of stratified sets. He has also developed a novel representation of object orientation basedon unnormalized quaternions which reduces the complexity of the algorithms and enhances theirpractical applicability.After dealing with the movers' problem, the book next attacks and derivesseveral lower bounds on extensions of the problem: finding the shortest path among polyhedralobstacles, planning with velocity limits, and compliant motion planning with uncertainty. Itintroduces a clever technique, "path encoding," that allows a proof of NP-hardness for the first twoproblems and then shows that the general form of compliant motion planning, a problem that is thefocus of a great deal of recent work in robotics, is non-deterministic exponential time hard. Cannyproves this result using a highly original construction.John Canny received his doctorate from MITAnd is an assistant professor in the Computer Science Division at the University of California,Berkeley. The Complexity of Robot Motion Planning is the winner of the 1987 ACM DoctoralDissertation Award.