Algebraic Combinatorics on Words by M. Lothaire
Algebraic Combinatorics on Words - Table of Contents
PART I: SEQUENCES & PATTERNS
- 1. Contents and Preface
- 2. Finite and Infinite Words
- 3. Sturmian Words and Factor Complexity
- 4. Unavoidable Patterns in Combinatorics
- 5. Sesquipowers and Repetition Factors
PART II: ALGEBRAIC MONOIDS & SYSTEMS
- 6. The Plactic Monoid and Young Tableaux
- 7. Variable-Length Codes Theory
- 8. Numeration Systems and Automata
- 9. Periodicity and Fine-Wilf Theorem
- 10. Centralizers of Noncommutative Series
PART III: STATISTICS & EQUATIONS
- 11. Transformations on Words and q-Calculus
- 12. Statistics on Permutations and Words
- 13. Makanin's Algorithm for Word Equations
- 14. Independent Systems of Equations
- 15. Bibliography and Index
What You Will Learn in Algebraic Combinatorics on Words
Algebraic Combinatorics on Words by M. Lothaire is an authoritative, multi-author monograph published by Cambridge University Press that establishes the definitive algebraic and combinatorial foundations of sequence theory, formal language theory, and string processing. This comprehensive volume guides readers through finite and infinite words, Sturmian sequences, unavoidable patterns, sesquipowers, the plactic monoid, variable-length codes, numeration systems, period structures, non-commutative polynomials, q-calculus transformations, permutation statistics, Makanin's algorithm, and systems of word equations with exceptional mathematical precision.
Designed for graduate students, theoretical computer scientists, algebraic combinatorists, cryptographers, and computational linguists, this foundational text unifies abstract algebraic structures with discrete sequences. Lothaire details step-by-step mathematical proofs for combinatorics on free monoids, Young tableaux bijections, word equation decision procedures, and numeration representations. Whether you are analyzing pattern avoidance algorithms, studying algebraic properties of factor complexity, or implementing string matching mathematics, this book offers an indispensable roadmap.
Recognized globally as the premier masterwork in theoretical string combinatorics, it stands as one of the best advanced books on combinatorics on words and discrete mathematics. By connecting abstract monoid theory directly to computer science algorithms, it serves as an essential tool for mastering word combinatorics and formal language algebra with confidence.
Book Details & Specifications
Title:
Algebraic Combinatorics on Words by M. Lothaire
Publisher:
Cambridge University Press
Year:
2011
Pages:
455
Type:
PDF
Language:
English
ISBN-10 #:
0521180716
ISBN-13 #:
978-0521180719
License:
External Educational Resource
Amazon:
Amazon
About the Author: M. Lothaire
The author M. Lothaire
is the collective pseudonym used by an international group of leading mathematicians and theoretical computer scientists, organized under the direction of Jean Berstel, Dominique Perrin, and their collaborators. The Lothaire group has authored the definitive series of foundational texts that established combinatorics on words as an independent mathematical discipline.
Through Algebraic Combinatorics on Words, Lothaire brings together world-renowned experts in algebraic combinatorics, formal languages, and theoretical computer science. The text's rigorous proof structures, comprehensive scope, and deep connections to representation theory make this volume a classic reference for combinatorics on words trusted by researchers worldwide.
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