Algebraic combinatorics on words

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Algebraic combinatorics on words / M. Lothaire

資料種別:: 図書
出版情報:: Cambridge : Cambridge University Press, 2002
形態:: xiii, 504 p. ; 25 cm
シリーズ名:: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 90 <BA00064663>
著者名:: Lothaire, M. <DA00034272>
ISBN:: 9780521812207 [0521812208]
書誌ID:: BA56423669

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注記:

Bibliography: p. 473-496
Includes indexes

主題:

Combinatorial analysis; Word problems (Mathematics)

言語:

英語

目次情報:

Preface

Finite and Infinite Words / Chapter 1：

Introduction / 1.0：

Semigroups / 1.1：

Words / 1.2：

Automata / 1.3：

Generating series / 1.4：

Symbolic dynamical systems / 1.5：

Unavoidable sets / 1.6：

Problems

Notes

Sturmian Words / Chapter 2：

Equivalent definitions / 2.0：

Standard words / 2.2：

Sturmian morphisms / 2.3：

Unavoidable Patterns / Chapter 3：

Definitions and basic properties / 3.0：

Deciding avoidability: the Zimin algorithm / 3.2：

Avoidability on a fixed alphabet / 3.3：

Sesquipowers / Chapter 4：

Bi-ideal sequences / 4.0：

Canonical factorizations / 4.2：

Sesquipowers and recurrence / 4.3：

Extensions of a theorem of Shirshov / 4.4：

Finiteness conditions for semigroups / 4.5：

The Plactic Monoid / Chapter 5：

Schensted's algorithm / 5.0：

Greene's invariants and the plactic monoid / 5.2：

The Robinson--Schensted--Knuth correspondence / 5.3：

Schur functions and the Littlewood--Richardson rule / 5.4：

Coplactic operations / 5.5：

Cyclage and canonical embeddings / 5.6：

Codes / Chapter 6：

X-factorizations / 6.0：

Defect / 6.2：

More defect / 6.3：

A theorem of Schutzenberger / 6.4：

Numeration Systems / Chapter 7：

Standard representation of numbers / 7.0：

Beta-expansions / 7.2：

U-representations / 7.3：

Representation of complex numbers / 7.4：

Periodicity / Chapter 8：

Periods in a finite word / 8.0：

Local versus global periodicity / 8.2：

Infinite words / 8.3：

Centralizers of Noncommutative Series and Polynomials / Chapter 9：

Cohn's centralizer theorem / 9.0：

Euclidean division and principal right ideals / 9.2：

Integral closure of the centralizer / 9.3：

Homomorphisms into k[t] / 9.4：

Bergman's centralizer theorem / 9.5：

Free subalgebras and the defect theorem / 9.6：

Appendix: some commutative algebra / 9.7：

Transformations on Words and q-Calculus / Chapter 10：

The q-binomial coefficients / 10.0：

The MacMahon Verfahren / 10.2：

The insertion technique / 10.3：

The (t, q)-factorial generating functions / 10.4：

Words and biwords / 10.5：

Commutations / 10.6：

The two commutations / 10.7：

The main algorithm / 10.8：

The inverse of the algorithm / 10.9：

Statistics on circuits / 10.10：

Statistics on words and equidistribution properties / 10.11：

Statistics on Permutations and Words / Chapter 11：

Preliminaries / 11.0：

Words with a given shape / 11.2：

Backsteps of permutations with a given shape / 11.3：

Inversions of permutations with a given shape / 11.4：

Lyndon factorization and cycles of permutations / 11.5：

Major index of permutations with a given cyclic type / 11.6：

Makanin's Algorithm / Chapter 12：

Words and word equations / 12.0：

The exponent of periodicity / 12.2：

Boundary equations / 12.3：

Proof of Theorem 12.3.10 / 12.4：

Independent Systems of Equations / Chapter 13：

Sets and equations / 13.0：

The compactness property / 13.2：

Independence of finite systems of equations / 13.3：

Semigroups without the compactness property / 13.4：

Semigroups with the compactness property / 13.5：

References

Index of Notation

General Index

Preface

Finite and Infinite Words / Chapter 1：

Introduction / 1.0：

Semigroups / 1.1：

Words / 1.2：

Automata / 1.3：

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