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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 linguistics. This volume is the first to attempt 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. Topics discussed include: Thue's square free words, Van der Waerden's theorem, Ramsey's theorem; factorization of free monoids including application to free Lie algebras; equations in words, etc.
Table of contents:
1. Words D. Perrin; 2. Square free words and idempotent semigroups J. Berstel and C. Reutenauer; 3. Van der Waerden's theorem J. E. Pin; 4. Repetitive mappings and morphisms G. Pirillo; 5. Factorizations of free monoids D. Perrin; 6. Subwords J. Sakarovitch and I. Simon; 7. Unavoidable irregularities in words M. P. Schützenberger; 8. The critical factorization theorem Choffrut; 9. Equations in words; 10. Rearrangements of words D. Foata; 11. Words and trees R. Cori.
Combinatorics on words, or finite sequences, is a field which grew simultaneously within disparate branches of mathematics such as group theory and probability. This classic volume is the first to attempt to present a thorough treatment of this theory.
This classic volume presents a thorough treatment of the theory of combinatorics on words.
Table of contents:
1. Words D. Perrin; 2. Square free words and idempotent semigroups J. Berstel and C. Reutenauer; 3. Van der Waerden's theorem J. E. Pin; 4. Repetitive mappings and morphisms G. Pirillo; 5. Factorizations of free monoids D. Perrin; 6. Subwords J. Sakarovitch and I. Simon; 7. Unavoidable irregularities in words M. P. Schützenberger; 8. The critical factorization theorem Choffrut; 9. Equations in words; 10. Rearrangements of words D. Foata; 11. Words and trees R. Cori.
Combinatorics on words, or finite sequences, is a field which grew simultaneously within disparate branches of mathematics such as group theory and probability. This classic volume is the first to attempt to present a thorough treatment of this theory.
This classic volume presents a thorough treatment of the theory of combinatorics on words.