The Surprising Mathematics Of Longest Increasing Subsequences

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The Surprising Mathematics of Longest Increasing Subsequences

Dan Romik
The Surprising Mathematics of Longest Increasing Subsequences Book PDF

Author : Dan Romik
Publisher : Cambridge University Press
Page : 366 pages
File Size : 54,8 Mb
Release : 2015-02-02
Category : Mathematics
ISBN : 9781107075832

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The Surprising Mathematics of Longest Increasing Subsequences by Dan Romik Pdf

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.

Combinatorics and Random Matrix Theory

Jinho Baik,Percy Deift,Toufic Suidan
Combinatorics and Random Matrix Theory Book PDF

Author : Jinho Baik,Percy Deift,Toufic Suidan
Publisher : American Mathematical Soc.
Page : 461 pages
File Size : 40,9 Mb
Release : 2016-06-22
Category : Combinatorial analysis
ISBN : 9780821848418

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Combinatorics and Random Matrix Theory by Jinho Baik,Percy Deift,Toufic Suidan Pdf

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

Cezar Câmpeanu,Florin Manea,Jeffrey Shallit
Descriptional Complexity of Formal Systems Book PDF

Author : Cezar Câmpeanu,Florin Manea,Jeffrey Shallit
Publisher : Springer
Page : 217 pages
File Size : 45,7 Mb
Release : 2016-07-13
Category : Mathematics
ISBN : 9783319411149

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Descriptional Complexity of Formal Systems by Cezar Câmpeanu,Florin Manea,Jeffrey Shallit Pdf

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

Costas Iliopoulos,Hon Wai Leong,Wing-Kin Sung
Combinatorial Algorithms Book PDF

Author : Costas Iliopoulos,Hon Wai Leong,Wing-Kin Sung
Publisher : Springer
Page : 388 pages
File Size : 54,7 Mb
Release : 2018-07-03
Category : Computers
ISBN : 9783319946672

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Combinatorial Algorithms by Costas Iliopoulos,Hon Wai Leong,Wing-Kin Sung Pdf

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.

Handbook of Enumerative Combinatorics

Miklos Bona
Handbook of Enumerative Combinatorics Book PDF

Author : Miklos Bona
Publisher : CRC Press
Page : 1073 pages
File Size : 49,6 Mb
Release : 2015-03-24
Category : Mathematics
ISBN : 9781482220865

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Handbook of Enumerative Combinatorics by Miklos Bona Pdf

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

An Introduction to Symmetric Functions and Their Combinatorics

Eric S. Egge
An Introduction to Symmetric Functions and Their Combinatorics Book PDF

Author : Eric S. Egge
Publisher : American Mathematical Soc.
Page : 342 pages
File Size : 53,5 Mb
Release : 2019-11-18
Category : Education
ISBN : 9781470448998

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An Introduction to Symmetric Functions and Their Combinatorics by Eric S. Egge Pdf

This book is a reader-friendly introduction to the theory of symmetric functions, and it includes fundamental topics such as the monomial, elementary, homogeneous, and Schur function bases; the skew Schur functions; the Jacobi–Trudi identities; the involution ω ω; the Hall inner product; Cauchy's formula; the RSK correspondence and how to implement it with both insertion and growth diagrams; the Pieri rules; the Murnaghan–Nakayama rule; Knuth equivalence; jeu de taquin; and the Littlewood–Richardson rule. The book also includes glimpses of recent developments and active areas of research, including Grothendieck polynomials, dual stable Grothendieck polynomials, Stanley's chromatic symmetric function, and Stanley's chromatic tree conjecture. Written in a conversational style, the book contains many motivating and illustrative examples. Whenever possible it takes a combinatorial approach, using bijections, involutions, and combinatorial ideas to prove algebraic results. The prerequisites for this book are minimal—familiarity with linear algebra, partitions, and generating functions is all one needs to get started. This makes the book accessible to a wide array of undergraduates interested in combinatorics.

Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)

Sirakov Boyan,Souza Paulo Ney De,Viana Marcelo
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes Book PDF

Author : Sirakov Boyan,Souza Paulo Ney De,Viana Marcelo
Publisher : World Scientific
Page : 5396 pages
File Size : 53,5 Mb
Release : 2019-02-27
Category : Mathematics
ISBN : 9789813272897

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Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by Sirakov Boyan,Souza Paulo Ney De,Viana Marcelo Pdf

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.

Combinatorial Pattern Matching

Ferdinando Cicalese,Ely Porat,Ugo Vaccaro
Combinatorial Pattern Matching Book PDF

Author : Ferdinando Cicalese,Ely Porat,Ugo Vaccaro
Publisher : Springer
Page : 412 pages
File Size : 51,6 Mb
Release : 2015-06-15
Category : Computers
ISBN : 9783319199290

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Combinatorial Pattern Matching by Ferdinando Cicalese,Ely Porat,Ugo Vaccaro Pdf

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.

Lectures on Random Lozenge Tilings

Vadim Gorin
Lectures on Random Lozenge Tilings Book PDF

Author : Vadim Gorin
Publisher : Cambridge University Press
Page : 261 pages
File Size : 49,9 Mb
Release : 2021-09-09
Category : Language Arts & Disciplines
ISBN : 9781108843966

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Lectures on Random Lozenge Tilings by Vadim Gorin Pdf

This is the first book dedicated to reviewing the mathematics of random tilings of large domains on the plane.

Introduction to Random Graphs

Alan Frieze,Michał Karoński
Introduction to Random Graphs Book PDF

Author : Alan Frieze,Michał Karoński
Publisher : Cambridge University Press
Page : 483 pages
File Size : 40,7 Mb
Release : 2016
Category : Mathematics
ISBN : 9781107118508

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Introduction to Random Graphs by Alan Frieze,Michał Karoński Pdf

The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.

Machines, Computations, and Universality

Jérôme Durand-Lose,Sergey Verlan
Machines Computations and Universality Book PDF

Author : Jérôme Durand-Lose,Sergey Verlan
Publisher : Springer
Page : 171 pages
File Size : 55,6 Mb
Release : 2018-06-04
Category : Computers
ISBN : 9783319924021

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Machines, Computations, and Universality by Jérôme Durand-Lose,Sergey Verlan Pdf

This book constitutes the refereed proceedings of the 8th International Conference on Machines, Computations, and Universality, MCU 2018, held in Fontainebleau, France, in June 2018. The 9 revised full papers presented together with 5 invited talks were carefully reviewed and selected from numerous submissions. MCU explores computation in the setting of various discrete models (Turing machines, register machines, cellular automata, tile assembly systems, rewriting systems, molecular computing models, neural models, concurrent systems, etc.) and analog and hybrid models (BSS machines, infinite time cellular automata, real machines, quantum computing, etc.).

Introduction to Malliavin Calculus

David Nualart,Eulalia Nualart
Introduction to Malliavin Calculus Book PDF

Author : David Nualart,Eulalia Nualart
Publisher : Cambridge University Press
Page : 249 pages
File Size : 43,8 Mb
Release : 2018-09-27
Category : Business & Economics
ISBN : 9781107039124

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Introduction to Malliavin Calculus by David Nualart,Eulalia Nualart Pdf

A compact introduction to this active and powerful area of research, combining basic theory, core techniques, and recent applications.

Applied Stochastic Differential Equations

Simo Särkkä,Arno Solin
Applied Stochastic Differential Equations Book PDF

Author : Simo Särkkä,Arno Solin
Publisher : Cambridge University Press
Page : 327 pages
File Size : 51,6 Mb
Release : 2019-05-02
Category : Business & Economics
ISBN : 9781316510087

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Applied Stochastic Differential Equations by Simo Särkkä,Arno Solin Pdf

With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Noise Sensitivity of Boolean Functions and Percolation

Christophe Garban,Jeffrey E. Steif
Noise Sensitivity of Boolean Functions and Percolation Book PDF

Author : Christophe Garban,Jeffrey E. Steif
Publisher : Cambridge University Press
Page : 223 pages
File Size : 49,9 Mb
Release : 2015
Category : Computers
ISBN : 9781107076433

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Noise Sensitivity of Boolean Functions and Percolation by Christophe Garban,Jeffrey E. Steif Pdf

This is the first book to cover the theory of noise sensitivity of Boolean functions with particular emphasis on critical percolation.

Computational Bayesian Statistics

M. Antónia Amaral Turkman,Carlos Daniel Paulino,Peter Müller
Computational Bayesian Statistics Book PDF

Author : M. Antónia Amaral Turkman,Carlos Daniel Paulino,Peter Müller
Publisher : Cambridge University Press
Page : 256 pages
File Size : 52,5 Mb
Release : 2019-02-28
Category : Business & Economics
ISBN : 9781108481038

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Computational Bayesian Statistics by M. Antónia Amaral Turkman,Carlos Daniel Paulino,Peter Müller Pdf

This integrated introduction to fundamentals, computation, and software is your key to understanding and using advanced Bayesian methods.