Advances In Combinatorial Mathematics
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Combinatorial Mathematics
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Author : Douglas B. West
language : en
Publisher: Cambridge University Press
Release Date : 2021
Combinatorial Mathematics written by Douglas B. West 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 with Mathematics categories.
This is the most readable and thorough graduate textbook and reference for combinatorics, covering enumeration, graphs, sets, and methods.
Analytic Combinatorics In Several Variables
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Author : Robin Pemantle
language : en
Publisher: Cambridge University Press
Release Date : 2013-05-31
Analytic Combinatorics In Several Variables written by Robin Pemantle 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 2013-05-31 with Mathematics categories.
Aimed at graduate students and researchers in enumerative combinatorics, this book is the first to treat the analytic aspects of combinatorial enumeration from a multivariate perspective.
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.
Combinatorics And Commutative Algebra
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Author : Richard P. Stanley
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-13
Combinatorics And Commutative Algebra written by Richard P. Stanley and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-13 with Mathematics categories.
Some remarkable connections between commutative algebra and combinatorics have been discovered in recent years. This book provides an overview of two of the main topics in this area. The first concerns the solutions of linear equations in nonnegative integers. Applications are given to the enumeration of integer stochastic matrices (or magic squares), the volume of polytopes, combinatorial reciprocity theorems, and related results. The second topic deals with the face ring of a simplicial complex, and includes a proof of the Upper Bound Conjecture for Spheres. An introductory chapter giving background information in algebra, combinatorics and topology broadens access to this material for non-specialists. New to this edition is a chapter surveying more recent work related to face rings, focusing on applications to f-vectors.
Advanced Combinatorics
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Author : Louis Comtet
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Advanced Combinatorics written by Louis Comtet and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Notwithstanding its title, the reader will not find in this book a systematic account of this huge subject. Certain classical aspects have been passed by, and the true title ought to be "Various questions of elementary combina torial analysis". For instance, we only touch upon the subject of graphs and configurations, but there exists a very extensive and good literature on this subject. For this we refer the reader to the bibliography at the end of the volume. The true beginnings of combinatorial analysis (also called combina tory analysis) coincide with the beginnings of probability theory in the 17th century. For about two centuries it vanished as an autonomous sub ject. But the advance of statistics, with an ever-increasing demand for configurations as well as the advent and development of computers, have, beyond doubt, contributed to reinstating this subject after such a long period of negligence. For a long time the aim of combinatorial analysis was to count the different ways of arranging objects under given circumstances. Hence, many of the traditional problems of analysis or geometry which are con cerned at a certain moment with finite structures, have a combinatorial character. Today, combinatorial analysis is also relevant to problems of existence, estimation and structuration, like all other parts of mathema tics, but exclusively forjinite sets.
Additive Combinatorics
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Author : Terence Tao
language : en
Publisher: Cambridge University Press
Release Date : 2006-09-14
Additive Combinatorics written by Terence Tao 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 2006-09-14 with Mathematics categories.
Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate-level 2006 text will allow students and researchers easy entry into this fascinating field. Here, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and providing immediate applications to problems in additive combinatorics. The power of these tools is well demonstrated in the presentation of recent advances such as Szemerédi's theorem on arithmetic progressions, the Kakeya conjecture and Erdos distance problems, and the developing field of sum-product estimates. The text is supplemented by a large number of exercises and new results.
Combinatorial Commutative Algebra
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Author : Ezra Miller
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-06-21
Combinatorial Commutative Algebra written by Ezra Miller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-21 with Mathematics categories.
Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs
Geometric Graphs And Arrangements
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Author : Stefan Felsner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Graphs And Arrangements written by Stefan Felsner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Among the intuitively appealing aspects of graph theory is its close connection to drawings and geometry. The development of computer technology has become a source of motivation to reconsider these connections, in particular geometric graphs are emerging as a new subfield of graph theory. Arrangements of points and lines are the objects for many challenging problems and surprising solutions in combinatorial geometry. The book is a collection of beautiful and mostly very recent results from the intersection of geometry, graph theory and combinatorics.
Advances In Combinatorial Methods And Applications To Probability And Statistics
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Author : N. Balakrishnan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Advances In Combinatorial Methods And Applications To Probability And Statistics written by N. Balakrishnan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Sri Gopal Mohanty has made pioneering contributions to lattice path counting and its applications to probability and statistics. This is clearly evident from his lifetime publications list and the numerous citations his publications have received over the past three decades. My association with him began in 1982 when I came to McMaster Univer sity. Since then, I have been associated with him on many different issues at professional as well as cultural levels; I have benefited greatly from him on both these grounds. I have enjoyed very much being his colleague in the statistics group here at McMaster University and also as his friend. While I admire him for his honesty, sincerity and dedication, I appreciate very much his kindness, modesty and broad-mindedness. Aside from our common interest in mathematics and statistics, we both have great love for Indian classical music and dance. We have spent numerous many different subjects associated with the Indian music and hours discussing dance. I still remember fondly the long drive (to Amherst, Massachusetts) I had a few years ago with him and his wife, Shantimayee, and all the hearty discussions we had during that journey. Combinatorics and applications of combinatorial methods in probability and statistics has become a very active and fertile area of research in the recent past.
Discrete And Combinatorial Mathematics
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Author : Ralph P. Grimaldi
language : en
Publisher: Addison Wesley Publishing Company
Release Date : 1993-10-01
Discrete And Combinatorial Mathematics written by Ralph P. Grimaldi and has been published by Addison Wesley Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-01 with Combinatorial analysis categories.