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Topics on Combinatorial Semigroups / by Yuqi Guo, Yun Liu, Shoufeng Wang.
Springer Nature - Springer Mathematics and Statistics eBooks 2024 English International Available online
View online- Format:
- Book
- Author/Creator:
- Guo, Yuqi.
- Series:
- Mathematics and Statistics Series
- Language:
- English
- Subjects (All):
- Group theory.
- Computer science--Mathematics.
- Computer science.
- Algebra, Universal.
- Associative rings.
- Associative algebras.
- Group Theory and Generalizations.
- Mathematical Applications in Computer Science.
- General Algebraic Systems.
- Associative Rings and Algebras.
- Local Subjects:
- Group Theory and Generalizations.
- Mathematical Applications in Computer Science.
- General Algebraic Systems.
- Associative Rings and Algebras.
- Physical Description:
- 1 online resource (279 pages)
- Edition:
- 1st ed. 2024.
- Place of Publication:
- Singapore : Springer Nature Singapore : Imprint: Springer, 2024.
- Summary:
- By combinatorial semigroups, we mean a general term of concepts, facts and methods which are produced in investigating of algebraic and combinatorial properties, constructions, classifications and interrelations of formal languages and automata, codes, finite and infinite words by using semigroup theory and combinatorial analysis. The main research objects in this field are the elements and subsets of the free semigroups and monoids and many combinatorial properties of these objects, which are closely related to algebraic theory of semigroups. This book first introduces some basic concepts and notations in combinatorial semigroups. Since many contents involving the constructions of (generalized) disjunctive languages and regular languages are closely related to the algebraic theory of codes, some selected topics are introduced in the following chapter, including the method of defining codes by using dependence systems, the maximality and completeness of codes, and the detailed discussion of some special kinds of codes such as convex codes, semaphore codes and solid codes. Then the remaining chapters present the main topics of the book - regular languages, disjunctive languages, and their various kinds of generalizations. This book might be useful to researchers in mathematics who are interested in combinatorial semigroups.
- Contents:
- Preface
- Basic Concepts and Notations
- Some Common-Used Codes
- Regular Languages
- Disjunctive Languages
- F-Disjunctive Languages
- Relatively Disjunctive (Regular) Languages
- Generalized Disjunctive Languages
- PS-Regular Languages.
- Notes:
- Description based on publisher supplied metadata and other sources.
- ISBN:
- 9789819991716
- OCLC:
- 1432006863
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