Topics On Combinatorial Semigroups
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Topics On Combinatorial Semigroups
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Author : Yuqi Guo
language : en
Publisher: Springer Nature
Release Date : 2024-04-22
Topics On Combinatorial Semigroups written by Yuqi Guo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-22 with Mathematics categories.
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.
Topics On Combinatorial Semigroups
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Author : 郭聿琦
language : en
Publisher:
Release Date : 2024
Topics On Combinatorial Semigroups written by 郭聿琦 and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with Combinatorial analysis categories.
Classical Finite Transformation Semigroups
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Author : Olexandr Ganyushkin
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-10
Classical Finite Transformation Semigroups written by Olexandr Ganyushkin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-10 with Mathematics categories.
The aim of this monograph is to give a self-contained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications. It covers the following topics on the examples of the three classical finite transformation semigroups: transformations and semigroups, ideals and Green's relations, subsemigroups, congruences, endomorphisms, nilpotent subsemigroups, presentations, actions on sets, linear representations, cross-sections and variants. The book contains many exercises and historical comments and is directed first of all to both graduate and postgraduate students looking for an introduction to the theory of transformation semigroups, but also to tutors and researchers.
Semigroups And Their Subsemigroup Lattices
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Author : L.N. Shevrin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Semigroups And Their Subsemigroup Lattices written by L.N. Shevrin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
0.1. General remarks. For any algebraic system A, the set SubA of all subsystems of A partially ordered by inclusion forms a lattice. This is the subsystem lattice of A. (In certain cases, such as that of semigroups, in order to have the right always to say that SubA is a lattice, we have to treat the empty set as a subsystem.) The study of various inter-relationships between systems and their subsystem lattices is a rather large field of investigation developed over many years. This trend was formed first in group theory; basic relevant information up to the early seventies is contained in the book [Suz] and the surveys [K Pek St], [Sad 2], [Ar Sad], there is also a quite recent book [Schm 2]. As another inspiring source, one should point out a branch of mathematics to which the book [Baer] was devoted. One of the key objects of examination in this branch is the subspace lattice of a vector space over a skew field. A more general approach deals with modules and their submodule lattices. Examining subsystem lattices for the case of modules as well as for rings and algebras (both associative and non-associative, in particular, Lie algebras) began more than thirty years ago; there are results on this subject also for lattices, Boolean algebras and some other types of algebraic systems, both concrete and general. A lot of works including several surveys have been published here.
Finiteness And Regularity In Semigroups And Formal Languages
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Author : Aldo de Luca
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Finiteness And Regularity In Semigroups And Formal Languages written by Aldo de Luca and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
The aim of this monograph is to present some recent research work on the combinatorial aspects of the theory of semigroups which are of great inter est for both algebra and theoretical computer science. This research mainly concerns that part of combinatorics of finite and infinite words over a finite alphabet which is usually called the theory of "unavoidable" regularities. The unavoidable regularities ofsufficiently large words over a finite alpha bet are very important in the study of finiteness conditions for semigroups. This problem consists in considering conditions which are satisfied by a fi nite semigroup and are such as to assure that a semigroup satisfying them is finite. The most natural requirement is that the semigroup is finitely gener ated. Ifone supposes that the semigroup is also periodic the study offiniteness conditions for these semigroups (or groups) is called the Burnside problem for semigroups (or groups). There exists an important relationship with the theory of finite automata because, as is well known, a language L over a fi nite alphabet is regular (that is, recognizable by a finite automaton) if and only if its syntactic monoid S(L) is finite. Hence, in principle, any finite ness condition for semigroups can be translated into a regularity condition for languages. The study of finiteness conditions for periodic languages (Le. , such that the syntactic semigroup is periodic) has been called the Burnside problem for languages.
Semigroups And Combinatorial Applications
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Author : Gerard Lallement
language : en
Publisher: John Wiley & Sons
Release Date : 1979
Semigroups And Combinatorial Applications written by Gerard Lallement and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.
The purpose of this book is to present those parts of the theory of semigroups that are directly related to automata theory, algebraic linguistics, and combinatorics. Publications in these mathematical disciplines contained methods and results pertaining to the algebraic theory of semigroups, and this has contributed to considerable enrichment of the theory, enlargement of its scope, and improved its potential to become a major domain of algebra. Semigroup theory appears to provide a general framework for unifying and clarifying a number of topics in fields that at first sight appear unrelated. This book is intended as a textbook for graduate students in mathematics and computer science, and as a reference book for researchers interested in associative structures.
Combinatorial Commutative Algebra
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Author : Ezra Miller
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-06-21
Combinatorial Commutative Algebra written by Ezra Miller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-21 with Mathematics categories.
Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs
Semigroups And Their Applications
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Author : Simon M. Goberstein
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Semigroups And Their Applications written by Simon M. Goberstein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Most papers published in this volume are based on lectures presented at the Chico Conference on Semigroups held on the Chico campus of the Cal ifornia State University on April 10-12, 1986. The conference was spon sored by the California State University, Chico in cooperation with the Engineering Computer Sciences Department of the Pacific Gas and Electric Company. The program included seven 50-minute addresses and seventeen 30-minute lectures. Speakers were invited by the organizing committee consisting of S. M. Goberstein and P. M. Higgins. The purpose of the conference was to bring together some of the leading researchers in the area of semigroup theory for a discussion of major recent developments in the field. The algebraic theory of semigroups is growing so rapidly and new important results are being produced at such a rate that the need for another meeting was well justified. It was hoped that the conference would help to disseminate new results more rapidly among those working in semi groups and related areas and that the exchange of ideas would stimulate research in the subject even further. These hopes were realized beyond all expectations.
Topics In Combinatorial Semigroup Theory
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Author : Victor Maltcev
language : en
Publisher:
Release Date : 2012
Topics In Combinatorial Semigroup Theory written by Victor Maltcev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Combinatorial group theory categories.
Semigroup Theory And Its Applications
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Author : Alfred Hoblitzelle Clifford
language : en
Publisher: Cambridge University Press
Release Date : 1996-05-16
Semigroup Theory And Its Applications written by Alfred Hoblitzelle Clifford and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-05-16 with Mathematics categories.
This volume contains survey papers by the invited speakers at the Conference on Semigroup Theory and Its Applications which took place at Tulane University in April, 1994. The authors represent the leading areas of research in semigroup theory and its applications, both to other areas of mathematics and to areas outside mathematics. Included are papers by Gordon Preston surveying Clifford's work on Clifford semigroups and by John Rhodes tracing the influence of Clifford's work on current semigroup theory. Notable among the areas of application are the paper by Jean-Eric Pin on applications of other areas of mathematics to semigroup theory and the paper by the editors on an application of semigroup theory to theoretical computer science and mathematical logic. All workers in semigroup theory will find this volume invaluable.