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Author : M. Lothaire
Publisher : Cambridge University Press
Page : 646 pages
File Size : 51,8 Mb
Release : 2005-07-11
Category : Computers
ISBN : 0521848024
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Author : M. Lothaire
Publisher : Cambridge University Press
Page : 260 pages
File Size : 46,9 Mb
Release : 1997-05-29
Category : Mathematics
ISBN : 9780521599245
Combinatorics on words, or finite sequences, is a field which grew simultaneously within disparate branches of mathematics such as group theory and probability. It has grown into an independent theory finding substantial applications in computer science automata theory and liguistics. This volume is the first to present a thorough treatment of this theory. All of the main results and techniques are covered. The presentation is accessible to undergraduate and graduate level students in mathematics and computer science as well as to specialists in all branches of applied mathematics.
Author : M. Lothaire
Publisher : Cambridge University Press
Page : 536 pages
File Size : 54,5 Mb
Release : 2002-04-18
Category : Mathematics
ISBN : 0521812208
Comprehensive 2002 introduction to combinatorics on words for mathematicians and theoretical computer scientists.
Author : Francine Blanchet-Sadri
Publisher : CRC Press
Page : 392 pages
File Size : 48,5 Mb
Release : 2007-11-19
Category : Mathematics
ISBN : 1420060937
The discrete mathematics and theoretical computer science communities have recently witnessed explosive growth in the area of algorithmic combinatorics on words. The next generation of research on combinatorics of partial words promises to have a substantial impact on molecular biology, nanotechnology, data communication, and DNA computing. Delving into this emerging research area, Algorithmic Combinatorics on Partial Words presents a mathematical treatment of combinatorics on partial words designed around algorithms and explores up-and-coming techniques for solving partial word problems as well as the future direction of research. This five-part book begins with a section on basics that covers terminology, the compatibility of partial words, and combinatorial properties of words. The book then focuses on three important concepts of periodicity on partial words: period, weak period, and local period. The next part describes a linear time algorithm to test primitivity on partial words and extends the results on unbordered words to unbordered partial words while the following section introduces some important properties of pcodes, details a variety of ways of defining and analyzing pcodes, and shows that the pcode property is decidable using two different techniques. In the final part, the author solves various equations on partial words, presents binary and ternary correlations, and covers unavoidable sets of partial words. Setting the tone for future research in this field, this book lucidly develops the central ideas and results of combinatorics on partial words.
Author : M. Lothaire
Publisher : Unknown
Page : 504 pages
File Size : 52,5 Mb
Release : 2002
Category : Combinatorial analysis
ISBN : 1107095875
Author : Philippe Flajolet,Robert Sedgewick
Publisher : Cambridge University Press
Page : 825 pages
File Size : 50,8 Mb
Release : 2009-01-15
Category : Mathematics
ISBN : 9781139477161
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.
Author : Fred Roberts,Barry Tesman
Publisher : CRC Press
Page : 889 pages
File Size : 45,7 Mb
Release : 2009-06-03
Category : Computers
ISBN : 9781420099836
Now with solutions to selected problems, Applied Combinatorics, Second Edition presents the tools of combinatorics from an applied point of view. This bestselling textbook offers numerous references to the literature of combinatorics and its applications that enable readers to delve more deeply into the topics.After introducing fundamental counting
Author : Alan Tucker
Publisher : Wiley
Page : 446 pages
File Size : 54,9 Mb
Release : 2003
Category : Combinatorial analysis
ISBN : 0471453021
This book is designed for use by students with a wide range of ability and maturity. The stronger the students, the harder the exercises that can be assigned. The book can be used for one-quarter, two-quarter, or one-semester course depending on how much material is used. Combinatorical reasoning underlies all analysis of computer systems. It plays a similar role in discrete operations research problems and in finite probability. This book teaches students in the mathematical sciences how to reason and model combinatorically. It seeks to develop proficiency in basic discrete math problem solving in the way that a calculus textbook develops proficiency in basic analysis problem solving. The three principle aspects of combinatorical reasoning emphasized in this book are: the systematic analysis of different possibilities, the exploration of the logical structure of a problem (e.g. finding manageable subpieces or first solving the problem with three objects instead of n), and ingenuity. Although important uses of combinatorics in computer science, operations research, and finite probability are mentioned, these applications are often used solely for motivation. Numerical examples involving the same concepts use more interesting settings such as poker probabilities or logical games.
Author : Silvia Heubach,Toufik Mansour
Publisher : CRC Press
Page : 504 pages
File Size : 49,7 Mb
Release : 2009-07-20
Category : Mathematics
ISBN : 1420072684
A One-Stop Source of Known Results, a Bibliography of Papers on the Subject, and Novel Research Directions Focusing on a very active area of research in the last decade, Combinatorics of Compositions and Words provides an introduction to the methods used in the combinatorics of pattern avoidance and pattern enumeration in compositions and words. It also presents various tools and approaches that are applicable to other areas of enumerative combinatorics. After a historical perspective on research in the area, the text introduces techniques to solve recurrence relations, including iteration and generating functions. It then focuses on enumeration of basic statistics for compositions. The text goes on to present results on pattern avoidance for subword, subsequence, and generalized patterns in compositions and then applies these results to words. The authors also cover automata, the ECO method, generating trees, and asymptotic results via random compositions and complex analysis. Highlighting both established and new results, this book explores numerous tools for enumerating patterns in compositions and words. It includes a comprehensive bibliography and incorporates the use of the computer algebra systems MapleTM and Mathematica®, as well as C++ to perform computations.
Author : Christophe Reutenauer
Publisher : Oxford University Press, USA
Page : 169 pages
File Size : 53,5 Mb
Release : 2019-01-15
Category : Mathematics
ISBN : 9780198827542
In 1875, Elwin Bruno Christoffel introduced a special class of words on a binary alphabet linked to continued fractions which would go onto be known as Christoffel words. Some years later, Andrey Markoff published his famous theory, the now called Markoff theory. It characterized certain quadratic forms and certain real numbers by extremal inequalities. Both classes are constructed using certain natural numbers known as Markoff numbers and they are characterized by a certain Diophantine equality. More basically, they are constructed using certain words essentially the Christoffel words. The link between Christoffel words and the theory of Markoff was noted by Ferdinand Frobenius in 1913, but has been neglected in recent times. Motivated by this overlooked connection, this book looks to expand on the relationship between these two areas. Part 1 focuses on the classical theory of Markoff, while Part II explores the more advanced and recent results of the theory of Christoffel words.
Author : Bruce E. Sagan
Publisher : American Mathematical Soc.
Page : 304 pages
File Size : 51,7 Mb
Release : 2020-10-16
Category : Education
ISBN : 9781470460327
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 : Nicholas Loehr
Publisher : CRC Press
Page : 600 pages
File Size : 47,8 Mb
Release : 2011-02-10
Category : Computers
ISBN : 9781439848869
Bijective proofs are some of the most elegant and powerful techniques in all of mathematics. Suitable for readers without prior background in algebra or combinatorics, Bijective Combinatorics presents a general introduction to enumerative and algebraic combinatorics that emphasizes bijective methods.The text systematically develops the mathematical
Author : Sergey Kitaev,Vadim Lozin
Publisher : Springer
Page : 264 pages
File Size : 41,6 Mb
Release : 2015-11-18
Category : Computers
ISBN : 9783319258591
This is the first comprehensive introduction to the theory of word-representable graphs, a generalization of several classical classes of graphs, and a new topic in discrete mathematics. After extensive introductory chapters that explain the context and consolidate the state of the art in this field, including a chapter on hereditary classes of graphs, the authors suggest a variety of problems and directions for further research, and they discuss interrelations of words and graphs in the literature by means other than word-representability. The book is self-contained, and is suitable for both reference and learning, with many chapters containing exercises and solutions to seleced problems. It will be valuable for researchers and graduate and advanced undergraduate students in discrete mathematics and theoretical computer science, in particular those engaged with graph theory and combinatorics, and also for specialists in algebra.
Author : Nicholas Loehr
Publisher : CRC Press
Page : 979 pages
File Size : 54,5 Mb
Release : 2017-08-10
Category : Mathematics
ISBN : 9781498780278
Combinatorics, Second Edition is a well-rounded, general introduction to the subjects of enumerative, bijective, and algebraic combinatorics. The textbook emphasizes bijective proofs, which provide elegant solutions to counting problems by setting up one-to-one correspondences between two sets of combinatorial objects. The author has written the textbook to be accessible to readers without any prior background in abstract algebra or combinatorics. Part I of the second edition develops an array of mathematical tools to solve counting problems: basic counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear algebraic methods. These tools are used to analyze combinatorial structures such as words, permutations, subsets, functions, graphs, trees, lattice paths, and much more. Part II cover topics in algebraic combinatorics including group actions, permutation statistics, symmetric functions, and tableau combinatorics. This edition provides greater coverage of the use of ordinary and exponential generating functions as a problem-solving tool. Along with two new chapters, several new sections, and improved exposition throughout, the textbook is brimming with many examples and exercises of various levels of difficulty.
Author : Valérie Berthé,Michel Rigo
Publisher : Cambridge University Press
Page : 496 pages
File Size : 52,5 Mb
Release : 2016-02-26
Category : Computers
ISBN : 9781107077027
Surveys trends arising from the applications and interactions between combinatorics, symbolic dynamics and theoretical computer science.