Algebraic combinatorics on words [EBook] / M. Lothaire.
Algebraic combinatorics on words [EBook] / M. Lothaire.
Combinatorics on words has arisen independently within several branches of mathematics, for instance number theory, group theory and probability, and appears frequently in problems related to theoretical computer science. The first unified treatment of the area was given in Lothaire's book Comb...
Personal Name(s):  Lothaire, M., (author) 

Imprint: 
Cambridge :
Cambridge University Press,
2002

Physical Description: 
1 online resource (xiii, 504 pages) 
Note: 
englisch 
ISBN: 
9781107326019 9780521180719 9780521812207 
Series Title: 
Encyclopedia of mathematics and its applications ;
volume 90 
Subject (LOC):  
Full Text 
Table of Contents:
 Finite and Infinite Words
 Semigroups
 Words
 Automata
 Generating series
 Symbolic dynamical systems
 Unavoidable sets
 Sturmian Words
 Equivalent definitions
 Standard words
 Sturmian morphisms
 Unavoidable Patterns
 Definitions and basic properties
 Deciding avoidability: the Zimin algorithm
 Avoidability on a fixed alphabet
 Sesquipowers
 Biideal sequences
 Canonical factorizations
 Sesquipowers and recurrence
 Extensions of a theorem of Shirshov
 Finiteness conditions for semigroups
 The Plactic Monoid
 Schensted's algorithm
 Greene's invariants and the plactic monoid
 The Robinson
 Schensted
 Knuth correspondence
 Schur functions and the Littlewood
 Richardson rule
 Coplactic operations
 Cyclage and canonical embeddings
 Codes
 Xfactorizations
 Defect
 More defect
 A theorem of Schutzenberger
 Numeration Systems
 Standard representation of numbers
 Betaexpansions
 Urepresentations
 Representation of complex numbers
 Periodicity
 Periods in a finite word
 Local versus global periodicity
 Infinite words
 Centralizers of Noncommutative Series and Polynomials
 Cohn's centralizer theorem
 Euclidean division and principal right ideals
 Integral closure of the centralizer
 Homomorphisms into k[t]
 Bergman's centralizer theorem
 Free subalgebras and the defect theorem
 Appendix: some commutative algebra
 Transformations on Words and qCalculus
 The qbinomial coefficients
 The MacMahon Verfahren.