The Diophantine Frobenius Problem

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The Diophantine Frobenius Problem

Author : Jorge L. Ramírez Alfonsín
Publisher : Oxford University Press, USA
ISBN 13 : 0198568207
Total Pages : 260 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis The Diophantine Frobenius Problem by : Jorge L. Ramírez Alfonsín

Download or read book The Diophantine Frobenius Problem written by Jorge L. Ramírez Alfonsín and published by Oxford University Press, USA. This book was released on 2005-12 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the early part of the last century, Ferdinand Georg Frobenius (1849-1917) raised he following problem, known as the Frobenius Problem (FP): given relatively prime positive integers a1,...,an, find the largest natural number (called the Frobenius number and denoted by g(a1,...,an) that is not representable as a nonnegative integer combination of a1,...,an, . At first glance FP may look deceptively specialized. Nevertheless it crops up again and again in the most unexpected places and has been extremely useful in investigating many different problems. A number of methods, from several areas of mathematics, have been used in the hope of finding a formula giving the Frobenius number and algorithms to calculate it. The main intention of this book is to highlight such methods, ideas, viewpoints and applications to a broader audience.

The Diophantine Frobenius Problem

Author : Jorge L. Ramírez Alfonsin
Publisher :
ISBN 13 : 9780191718229
Total Pages : 243 pages
Book Rating : 4.7/5 (182 download)

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Book Synopsis The Diophantine Frobenius Problem by : Jorge L. Ramírez Alfonsin

Download or read book The Diophantine Frobenius Problem written by Jorge L. Ramírez Alfonsin and published by . This book was released on 2005 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: A number of methods, from several areas of mathematics have been used in the hope of finding a formula giving the Frobenius number and algorithms to calculate it. The main intention of this book is to highlight these viewpoints, ideas and applications to a broader audience.

The Diophantine Frobenius Problem

Author : Jorge L. Ramírez Alfonsín
Publisher : OUP Oxford
ISBN 13 : 0191524484
Total Pages : 260 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis The Diophantine Frobenius Problem by : Jorge L. Ramírez Alfonsín

Download or read book The Diophantine Frobenius Problem written by Jorge L. Ramírez Alfonsín and published by OUP Oxford. This book was released on 2005-12-01 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the early part of the last century, Ferdinand Georg Frobenius (1849-1917) raised he following problem, known as the Frobenius Problem (FP): given relatively prime positive integers a1,...,an, find the largest natural number (called the Frobenius number and denoted by g(a1,...,an) that is not representable as a nonnegative integer combination of a1,...,an, . At first glance FP may look deceptively specialized. Nevertheless it crops up again and again in the most unexpected places and has been extremely useful in investigating many different problems. A number of methods, from several areas of mathematics, have been used in the hope of finding a formula giving the Frobenius number and algorithms to calculate it. The main intention of this book is to highlight such methods, ideas, viewpoints and applications to a broader audience.

The Diophantine Problem of Frobenius

Author : H. Krawczyk
Publisher :
ISBN 13 :
Total Pages : 4 pages
Book Rating : 4.:/5 (475 download)

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Book Synopsis The Diophantine Problem of Frobenius by : H. Krawczyk

Download or read book The Diophantine Problem of Frobenius written by H. Krawczyk and published by . This book was released on 1987 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computing the Continuous Discretely

Author : Matthias Beck
Publisher : Springer
ISBN 13 : 1493929690
Total Pages : 295 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Computing the Continuous Discretely by : Matthias Beck

Download or read book Computing the Continuous Discretely written by Matthias Beck and published by Springer. This book was released on 2015-11-14 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device. The topics include a friendly invitation to Ehrhart’s theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler–Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more. With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume? Reviews of the first edition: “You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.” — MAA Reviews “The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate rial, exercises, open problems and an extensive bibliography.” — Zentralblatt MATH “This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.” — Mathematical Reviews “Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.” — CHOICE

On a Linear Diophantine Problem of Frobenius

Author : Stefan Matthias Ritter
Publisher :
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4.:/5 (174 download)

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Book Synopsis On a Linear Diophantine Problem of Frobenius by : Stefan Matthias Ritter

Download or read book On a Linear Diophantine Problem of Frobenius written by Stefan Matthias Ritter and published by . This book was released on 1998 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Extending the Linear Diophantine Problem

Author : Curtis Kifer
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783845405131
Total Pages : 64 pages
Book Rating : 4.4/5 (51 download)

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Book Synopsis Extending the Linear Diophantine Problem by : Curtis Kifer

Download or read book Extending the Linear Diophantine Problem written by Curtis Kifer and published by LAP Lambert Academic Publishing. This book was released on 2011-09 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given integer-valued relatively prime coins' a1; a2; : ak, the Frobenius number is the largest integer n such that the linear diophantine equation a1m1 + a2m2 +::: + akmk = n has no solution in non-negative integers m1;m2; : mk. We denote by g(a1; : ak) the largest integer value not attainable by this coin system. That is to say that any integer x greater than the Frobenius number g(a1; : ak) has a representation x = a1x1 + a2x2 +::: + akxk by a1; a2; : ak for some non-negative integers x1; x2; : xk. We say x is representable by a1; a2; : ak. While it is obvious that there are representable positive integers and non-representable positive integers, must there be a largest non-representable integer? Maybe there are indefinitely large non-representable integers for a1; a2; : ak with gcd (a1; a2; : ak) = 1. This notion of whether or not the Frobenius number is well-defined will be the first bit of mathematics we look at in this paper. Proposition 1.1. The Frobenius number g(a1; : ak) is well-defined. Proof. Given a1; a2; : ak with gcd (a1; a2; : ak) = 1, the extended Euclidean algorithm gives that there exist m1;m2; : mk 2 Z such that...

On a Linear Diophantine Problem of Frobenius for Three Variables

Author : Bharti Temkin
Publisher :
ISBN 13 :
Total Pages : 238 pages
Book Rating : 4.:/5 (762 download)

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Book Synopsis On a Linear Diophantine Problem of Frobenius for Three Variables by : Bharti Temkin

Download or read book On a Linear Diophantine Problem of Frobenius for Three Variables written by Bharti Temkin and published by . This book was released on 1983 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Extending the Linear Diophantine Problem of Frobenius

Author : Curtis Kifer
Publisher :
ISBN 13 :
Total Pages : 100 pages
Book Rating : 4.:/5 (664 download)

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Book Synopsis Extending the Linear Diophantine Problem of Frobenius by : Curtis Kifer

Download or read book Extending the Linear Diophantine Problem of Frobenius written by Curtis Kifer and published by . This book was released on 2010 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to Diophantine Equations

Author : Titu Andreescu
Publisher : Springer Science & Business Media
ISBN 13 : 0817645497
Total Pages : 350 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis An Introduction to Diophantine Equations by : Titu Andreescu

Download or read book An Introduction to Diophantine Equations written by Titu Andreescu and published by Springer Science & Business Media. This book was released on 2010-09-02 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants — including Olympiad and Putnam competitors — as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.

Developments in Language Theory

Author : Masami Ito
Publisher : Springer
ISBN 13 : 354085780X
Total Pages : 555 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Developments in Language Theory by : Masami Ito

Download or read book Developments in Language Theory written by Masami Ito and published by Springer. This book was released on 2008-09-10 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 12th International Conference on Developments in Language Theory, DLT 2008, held in Kyoto, Japan, September 2008. The 36 revised full papers presented together with 6 invited papers were carefully reviewed and selected from 102 submissions. All important issues in language theory are addressed including grammars, acceptors and transducers for words, trees and graphs; algebraic theories of automata; algorithmic, combinatorial and algebraic properties of words and languages; variable length codes; symbolic dynamics; cellular automata; polyominoes and multidimensional patterns; decidability questions; image manipulation and compression; efficient text algorithms; relationships to cryptography, concurrency, complexity theory and logic; bio-inspired computing; quantum computing.

Numerical Semigroups

Author : J.C. Rosales
Publisher : Springer Science & Business Media
ISBN 13 : 1441901604
Total Pages : 186 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Numerical Semigroups by : J.C. Rosales

Download or read book Numerical Semigroups written by J.C. Rosales and published by Springer Science & Business Media. This book was released on 2009-12-24 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Numerical Semigroups" is the first monograph devoted exclusively to the development of the theory of numerical semigroups. This concise, self-contained text is accessible to first year graduate students, giving the full background needed for readers unfamiliar with the topic. Researchers will find the tools presented useful in producing examples and counterexamples in other fields such as algebraic geometry, number theory, and linear programming.

Algorithms and Discrete Applied Mathematics

Author : Subrahmanyam Kalyanasundaram
Publisher : Springer Nature
ISBN 13 : 3031522133
Total Pages : 338 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis Algorithms and Discrete Applied Mathematics by : Subrahmanyam Kalyanasundaram

Download or read book Algorithms and Discrete Applied Mathematics written by Subrahmanyam Kalyanasundaram and published by Springer Nature. This book was released on 2024-01-13 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 10th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2024, held in Bhilai, India during February 15–17, 2024. The 22 full papers included in this book were carefully reviewed and selected from 57 submissions. They were organized in topical sections as follows: Algorithms and Complexity; Computational Geometry; Discrete Applied Mathematics; Graph Algorithms; Graph Theory.

Intelligent Computing

Author : Kohei Arai
Publisher : Springer Nature
ISBN 13 : 3030801195
Total Pages : 1184 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Intelligent Computing by : Kohei Arai

Download or read book Intelligent Computing written by Kohei Arai and published by Springer Nature. This book was released on 2021-07-12 with total page 1184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive collection of chapters focusing on the core areas of computing and their further applications in the real world. Each chapter is a paper presented at the Computing Conference 2021 held on 15-16 July 2021. Computing 2021 attracted a total of 638 submissions which underwent a double-blind peer review process. Of those 638 submissions, 235 submissions have been selected to be included in this book. The goal of this conference is to give a platform to researchers with fundamental contributions and to be a premier venue for academic and industry practitioners to share new ideas and development experiences. We hope that readers find this volume interesting and valuable as it provides the state-of-the-art intelligent methods and techniques for solving real-world problems. We also expect that the conference and its publications is a trigger for further related research and technology improvements in this important subject.

Unsolved Problems in Number Theory

Author : Richard Guy
Publisher : Springer Science & Business Media
ISBN 13 : 0387266771
Total Pages : 455 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Unsolved Problems in Number Theory by : Richard Guy

Download or read book Unsolved Problems in Number Theory written by Richard Guy and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloane’s Online Encyclopedia of Integer Sequences, at the end of several of the sections.

Fundamentals of Computation Theory

Author : Zoltan Esik
Publisher : Springer Science & Business Media
ISBN 13 : 9783540571636
Total Pages : 488 pages
Book Rating : 4.5/5 (716 download)

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Book Synopsis Fundamentals of Computation Theory by : Zoltan Esik

Download or read book Fundamentals of Computation Theory written by Zoltan Esik and published by Springer Science & Business Media. This book was released on 1993-08-04 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Ninth Conference on Fundamentalsof Computation Theory (FCT 93) held in Szeged, Hungary, in August 1993. The conference was devoted to a broad range of topics including: - Semanticsand logical concepts in the theory of computing and formal specification - Automata and formal languages - Computational geometry, algorithmic aspects of algebra and algebraic geometry, cryptography - Complexity (sequential, parallel, distributed computing, structure, lower bounds, complexity of analytical problems, general concepts) - Algorithms (efficient, probabilistic, parallel, sequential, distributed) - Counting and combinatorics in connection with mathematical computer science The volume contains the texts of 8 invitedlectures and 32 short communications selected by the international program committee from a large number of submitted papers.

Mathematical Geophysics

Author : Jean-Yves Chemin
Publisher : Oxford University Press
ISBN 13 : 019857133X
Total Pages : 263 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis Mathematical Geophysics by : Jean-Yves Chemin

Download or read book Mathematical Geophysics written by Jean-Yves Chemin and published by Oxford University Press. This book was released on 2006-04-13 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at graduate students and researchers in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The Navier-Stokes equations are examined in both incompressible and rapidly rotating forms.