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Author: Dan Romik
Publisher: Cambridge University Press
ISBN: 1107075831
Category : Mathematics
Languages : en
Pages : 366
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Book Description
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.
Author: Dan Romik
Publisher: Cambridge University Press
ISBN: 1107075831
Category : Mathematics
Languages : en
Pages : 366
Get Book Here
Book Description
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.
Author: Laura Kovács
Publisher: Springer Nature
ISBN: 3031726219
Category :
Languages : en
Pages : 251
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Book Description
Author: Jinho Baik
Publisher: American Mathematical Soc.
ISBN: 0821848410
Category : Mathematics
Languages : en
Pages : 478
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Book Description
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.
Author: Günter Last
Publisher: Cambridge University Press
ISBN: 1107088011
Category : Mathematics
Languages : en
Pages : 315
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Book Description
A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.
Author: Cezar Câmpeanu
Publisher: Springer
ISBN: 3319411144
Category : Mathematics
Languages : en
Pages : 233
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Book Description
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.
Author: Costas Iliopoulos
Publisher: Springer
ISBN: 3319946676
Category : Computers
Languages : en
Pages : 405
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Book Description
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.
Author: Miklos Bona
Publisher: CRC Press
ISBN: 1482220865
Category : Mathematics
Languages : en
Pages : 1073
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Book Description
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
Author: Boyan Sirakov
Publisher: World Scientific
ISBN: 9813272899
Category : Mathematics
Languages : en
Pages : 5393
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Book Description
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.
Author: Bruce E. Sagan
Publisher: American Mathematical Soc.
ISBN: 1470460327
Category : Education
Languages : en
Pages : 304
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Book Description
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: Ferdinando Cicalese
Publisher: Springer
ISBN: 3319199293
Category : Computers
Languages : en
Pages : 429
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Book Description
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.
