The Surprising Mathematics Of Longest Increasing Subsequences
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The Surprising Mathematics Of Longest Increasing Subsequences
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Author : Dan Romik
language : en
Publisher: Cambridge University Press
Release Date : 2015-02-02
The Surprising Mathematics Of Longest Increasing Subsequences written by Dan Romik 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 2015-02-02 with Mathematics categories.
In a surprising sequence of developments, the longest increasing subsequence problem, originally mentioned as merely a curious example in a 1961 paper, has proven to have deep connections to many seemingly unrelated branches of mathematics, such as random permutations, random matrices, Young tableaux, and the corner growth model. The detailed and playful study of these connections makes this book suitable as a starting point for a wider exploration of elegant mathematical ideas that are of interest to every mathematician and to many computer scientists, physicists and statisticians. The specific topics covered are the Vershik-Kerov-Logan-Shepp limit shape theorem, the Baik-Deift-Johansson theorem, the Tracy-Widom distribution, and the corner growth process. This exciting body of work, encompassing important advances in probability and combinatorics over the last forty years, is made accessible to a general graduate-level audience for the first time in a highly polished presentation.
Reachability Problems
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Author : Laura Kovács
language : en
Publisher: Springer Nature
Release Date : 2024-09-19
Reachability Problems written by Laura Kovács and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-19 with Computers categories.
This book constitutes the proceedings of the 18th International Conference on Reachability Problems, RP 2024, which took place in Vienna, Austria, during September 25–27, 2024. The 13 full papers included in these proceedings were carefully reviewed and selected from 37 submissions. The book also contains two invited talks in full paper length. The contributions in these proceedings cover topics from computability and reachability; automata and complexity; linear systems and recurrences; and games and abstractions.
Combinatorics And Random Matrix Theory
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Author : Jinho Baik
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-06-22
Combinatorics And Random Matrix Theory written by Jinho Baik and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-22 with Mathematics categories.
Over the last fifteen years a variety of problems in combinatorics have been solved in terms of random matrix theory. More precisely, the situation is as follows: the problems at hand are probabilistic in nature and, in an appropriate scaling limit, it turns out that certain key quantities associated with these problems behave statistically like the eigenvalues of a (large) random matrix. Said differently, random matrix theory provides a “stochastic special function theory” for a broad and growing class of problems in combinatorics. The goal of this book is to analyze in detail two key examples of this phenomenon, viz., Ulam's problem for increasing subsequences of random permutations and domino tilings of the Aztec diamond. Other examples are also described along the way, but in less detail. Techniques from many different areas in mathematics are needed to analyze these problems. These areas include combinatorics, probability theory, functional analysis, complex analysis, and the theory of integrable systems. The book is self-contained, and along the way we develop enough of the theory we need from each area that a general reader with, say, two or three years experience in graduate school can learn the subject directly from the text.
Descriptional Complexity Of Formal Systems
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Author : Cezar Câmpeanu
language : en
Publisher: Springer
Release Date : 2016-07-13
Descriptional Complexity Of Formal Systems written by Cezar Câmpeanu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-13 with Mathematics categories.
his book constitutes the refereed proceedings of the 18th International Conference on Descriptional Complexity of Formal Systems, DCFS 2016, held in Bucharest, Romania, in July 2016. The 13 full papers presented together with 4 invited talks were carefully reviewed and selected from 21 submissions.Descriptional Complexity is a field in Computer Science that deals with the size of all kind of objects that occur in computational models, such as Turing Machines, finte automata, grammars, splicing systems and others. The topics of this conference are related to all aspects of descriptional complexity.
Combinatorial Algorithms
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Author : Costas Iliopoulos
language : en
Publisher: Springer
Release Date : 2018-07-03
Combinatorial Algorithms written by Costas Iliopoulos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-03 with Computers categories.
This book constitutes the refereed post-conference proceedings of the 29th International Workshop on Combinatorial Algorithms, IWOCA 2018, held in Singapore, Singapore, in July 2018. The 31 regular papers presented in this volume were carefully reviewed and selected from 69 submissions. They cover diverse areas of combinatorical algorithms, complexity theory, graph theory and combinatorics, combinatorial optimization, cryptography and information security, algorithms on strings and graphs, graph drawing and labelling, computational algebra and geometry, computational biology, probabilistic and randomised algorithms, algorithms for big data analytics, and new paradigms of computation.
Combinatorial Pattern Matching
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Author : Ferdinando Cicalese
language : en
Publisher: Springer
Release Date : 2015-06-15
Combinatorial Pattern Matching written by Ferdinando Cicalese and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-15 with Computers categories.
This book constitutes the refereed proceedings of the 26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015, held on Ischia Island, Italy, in June/July 2015. The 34 revised full papers presented together with 3 invited talks were carefully reviewed and selected from 83 submissions. The papers address issues of searching and matching strings and more complicated patterns such as trees; regular expressions; graphs; point sets; and arrays. The goal is to derive combinatorial properties of such structures and to exploit these properties in order to achieve superior performance for the corresponding computational problems. The meeting also deals with problems in computational biology; data compression and data mining; coding; information retrieval; natural language processing; and pattern recognition.
Handbook Of Enumerative Combinatorics
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Author : Miklos Bona
language : en
Publisher: CRC Press
Release Date : 2015-03-24
Handbook Of Enumerative Combinatorics written by Miklos Bona and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-24 with Mathematics categories.
Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today's most prominent researchers. The contributors survey the methods of combinatorial enumeration along with the most frequent applications of these methods.This important new work is edited by Miklos Bona of the University of Florida where he
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes
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Author : Boyan Sirakov
language : en
Publisher: World Scientific
Release Date : 2019-02-27
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes written by Boyan Sirakov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-27 with Mathematics categories.
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
The Thermodynamics Of Mathematical Representation
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Author : Daniel J. Graham
language : en
Publisher: CRC Press
Release Date : 2025-06-30
The Thermodynamics Of Mathematical Representation written by Daniel J. Graham and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-30 with Science categories.
Thermodynamics is the physical science surrounding work, heat, and relationships across fundamental quantities, and situates itself near the center of multiple disciplines through its generality and timelessness. Its laws required no rewriting after the twentieth century revolutions of quantum mechanics, relativity, and solid state physics, just to name three subjects. The nine chapters of this book make appeal to thermodynamic notions and laws to get under the hood of mathematics—the language of the physical sciences—without just echoing things best said and written in math books. It takes a system to learn about another system—we all need thermometers, voltmeters, and other gadgets to get to know objects of interest. But just as critical are the numbers and functions we put to the task, however relegated they are to computers in the modern day for the heavy lifting. To be sure, mathematical representations like x = 1⁄2, 5.2, π, e, etc., and f(x) = x2, sin(x), etc., are never in physical contact with the solids, liquids, and gases that draw our attention, but they are as impacted by the same natural laws as the lab apparatus itself. This book shows how the thermodynamic laws impact our number systems. The laws affirm that we have direct access to a vanishingly small fraction of the real numbers. They further establish that the real numbers present a maximum-evolved system impacting all matters of computation, graphing, differentiation, and integration. For completeness, one of the chapters includes cases where the thermodynamic laws have little, if anything, constructive to say about representations in mathematics. This book presents a novel perspective to students and teachers in the physical sciences, biology, and mathematics, with the goal of enriching classroom and seminar hours. The chapters are self-contained and written informally, and readers with rudimentary knowledge of energy, numbers, and functions should handle the material well.
Lectures On Random Lozenge Tilings
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Author : Vadim Gorin
language : en
Publisher: Cambridge University Press
Release Date : 2021-09-09
Lectures On Random Lozenge Tilings written by Vadim Gorin 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 2021-09-09 with Language Arts & Disciplines categories.
This is the first book dedicated to reviewing the mathematics of random tilings of large domains on the plane.