Algebraic combinatorics on words [E-Book] / M. Lothaire.
Lothaire, M., (author)
Cambridge : Cambridge University Press, 2002
1 online resource (xiii, 504 pages)
englisch
9781107326019
9780521180719
9780521812207
Encyclopedia of mathematics and its applications ; volume 90
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
  • Bi-ideal 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
  • X-factorizations
  • Defect
  • More defect
  • A theorem of Schutzenberger
  • Numeration Systems
  • Standard representation of numbers
  • Beta-expansions
  • U-representations
  • 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 q-Calculus
  • The q-binomial coefficients
  • The MacMahon Verfahren.