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1.

図書

図書
Jan Mycielski, Grzegorz Rozenberg, Arto Salomaa (eds.)
出版情報: Berlin : Springer, c1997  x, 370 p. ; 24 cm
シリーズ名: Lecture notes in computer science ; 1261
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2.

図書

図書
A. Ehrenfeucht, T. Harju, G. Rozenberg
出版情報: Singapore : World Scientific, c1999  xvi, 290 p. ; 23 cm
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目次情報: 続きを見る
Preface
Preliminaries / Chapter 1:
Notations / 1.1:
Sets and functions / 1.1.1:
Closure operators / 1.1.2:
Relations / 1.1.3:
Equivalence relations / 1.1.4:
Partial orders / 1.2:
Downsets / 1.2.1:
Order embeddings / 1.2.2:
Linear orders / 1.2.3:
Semigroups and groups / 1.3:
Notations for semigroups and monoids / 1.3.1:
Free monoids (with involution) / 1.3.2:
Preliminaries on groups / 1.3.3:
Group actions / 1.3.4:
Free groups, commutators and verbal identities / 1.3.5:
Graph Theoretical Preliminaries / Chapter 2:
Directed and Undirected Graphs / 2.1:
Basic notions / 2.1.1:
Connectivity of graphs / 2.1.2:
Some special graphs / 2.1.3:
Comparability graphs / 2.2:
Transitively oriented graphs / 2.2.1:
Permutation graphs and cographs / 2.2.2:
Construction trees of cographs / 2.2.3:
2-Structures and Their Clans / Chapter 3:
Introduction and representations / 3.1:
Definition of a 2-structure / 3.1.1:
Isomorphic 2-structures / 3.1.2:
Reversibility / 3.1.3:
Substructures and clans / 3.2:
Substructures, clans and factors / 3.2.1:
Refinements and similarity / 3.2.2:
Reversible version / 3.2.3:
Graphs and packed components / 3.2.4:
Some special 2-structures / 3.2.5:
Closure properties of clans / 3.3:
Basic closures / 3.3.1:
Sibas: set theoretic closure properties / 3.3.2:
Clans of factors / 3.3.3:
Prime clans / 3.4:
Prime members in sibas / 3.4.1:
Minimal overlapping clans / 3.4.2:
Quotients and Homomorphisms / Chapter 4:
Quotients / 4.1:
Factorizations and quotients / 4.1.1:
Homomorphisms / 4.1.2:
Natural epimorphisms and decompositions / 4.1.3:
Clans and epimorphisms / 4.2:
Homomorphism theorem / 4.2.1:
Prime clans in quotients / 4.2.2:
Primitive quotients / 4.2.3:
Other operations / 4.3:
Premorphisms / 4.3.1:
Extensions / 4.3.2:
Clan Decomposition / Chapter 5:
The clan decomposition theorem / 5.1:
Maximal prime clans / 5.1.1:
Special sibas and 2-structures / 5.1.2:
The relationship of sibas to 2-structures / 5.1.3:
The shape of a 2-structure / 5.2:
The shape and its representation as a tree / 5.2.1:
Same shapes / 5.2.2:
A construction of prime clans / 5.3:
A construction of clans / 5.3.1:
Primitive 2-Structures / 5.3.2:
Small primitive substructures / 6.1:
Uniformly imprimitive 2-structures / 6.1.1:
Primitive substructures of 3 or 4 nodes / 6.1.2:
Hereditary properties / 6.2:
Local and global nodes / 6.2.1:
Critically primitive 2-structures / 6.2.2:
The parity theorem / 6.3.1:
The list of critically primitive 2-structures / 6.3.2:
Angular 2-Structures / Chapter 7:
Angularity / 7.1:
All-connectivity / 7.1.1:
All-connected skew angular 2-structures / 7.1.2:
T-structures / 7.2:
T-structures and partial orders / 7.2.1:
T[subscript 2]-structures / 7.2.2:
Linear orders and Schroder numbers / 7.3:
Bi-orders and linear orders / 7.3.1:
Uniformly imprimitive linear orders / 7.3.2:
Parenthesis words and Schroder numbers / 7.3.3:
Labelled 2-Structures / Chapter 8:
Introduction to l2-structures / 8.1:
Definitions / 8.1.1:
Substructures, clans and quotients / 8.1.2:
Clan decomposition of l2-structures / 8.2:
Uniqueness of decompositions / 8.2.1:
The shape of an l2-structure / 8.2.2:
Graphs and their representations / 8.2.3:
Graphs as l2-structures / 8.3.1:
On comparability graphs / 8.3.2:
Unstable Labelled 2-Structures / Chapter 9:
Triangle free and unstable l2-structures / 9.1:
Removable edges / 9.1.1:
Internal and external nodes / 9.1.2:
Triangle-free l2-structures / 9.1.3:
Heredity in unstable l2-structures / 9.2:
The partition of nodes / 9.2.1:
Alternating structures / 9.2.2:
Degrees of nodes / 9.2.3:
A composition of unstable l2-structures / 9.3:
A constructive reduction of primitive l2-structures / 9.3.1:
Pendant components / 9.3.2:
Automorphisms of Labelled 2-Structures / Chapter 10:
Label preserving automorphisms / 10.1:
The l-automorphism groups / 10.1.1:
Transitivity / 10.1.2:
Automorphic actions on factors / 10.1.3:
Universality of l-automorphism groups / 10.1.4:
Nonpreserving automorphisms / 10.2:
Connections to l-automorphisms / 10.2.1:
Transitivity and associated permutations / 10.2.2:
Representing labels by automorphisms / 10.2.3:
Switching of Graphs / Chapter 11:
Introduction to switching / 11.1:
The group of graphs / 11.1.1:
Switching classes / 11.1.3:
Structural properties of switching classes / 11.2:
A local characterization / 11.2.1:
Automorphisms / 11.2.2:
Special problems on undirected graphs / 11.3:
Two-graphs / 11.3.1:
Eulerian graphs / 11.3.2:
Pancyclic graphs / 11.3.3:
Trees / 11.3.4:
Labelled Structures over Groups / Chapter 12:
Introduction / 12.1:
Groups and involutions / 12.1.1:
Selectors and switching classes / 12.1.2:
An interpretation in networks / 12.2:
Concurrent behaviour in networks / 12.2.1:
Reducing the actions to groups / 12.2.2:
Introducing reversibility / 12.2.3:
Examples for some special groups / 12.3:
The cyclic groups Z[subscript 3] and Z[subscript 4] / 12.3.1:
The symmetric group S[subscript 3] / 12.3.2:
Clans of Switching Classes / Chapter 13:
Associated groups / 13.1:
The group of selectors / 13.1.1:
The group of abelian switching classes / 13.1.2:
Clans and horizons / 13.2:
Spanning trees / 13.2.1:
Horizons and constant selectors / 13.2.2:
Clans / 13.2.3:
Cardinalities of switching classes / 13.3:
Some special cases / 13.3.1:
Centralizers / 13.3.2:
Some improvements / 13.3.3:
Quotients and Plane Trees / Chapter 14:
Quotients of switching classes / 14.1:
Planes and plane trees / 14.1.1:
Planes / 14.2.1:
Plane trees / 14.2.2:
Bijective correspondence of plane trees / 14.2.3:
Forms / 14.2.4:
Invariants / Chapter 15:
Free invariants / 15.1:
General invariants / 15.1.1:
Edge monoids / 15.1.2:
Variable functions and free invariants / 15.1.3:
Group properties of free invariants / 15.2:
Abelian property / 15.2.1:
Graphs of words / 15.2.2:
Verbal identities / 15.2.3:
Invariants on abelian groups / 15.3:
Independency of free invariants / 15.3.1:
Complete sets of invariants / 15.3.2:
Invariants on nonabelian groups / 15.4:
General observations / 15.4.1:
Central characters / 15.4.2:
A characterization theorem / 15.4.3:
Bibliography
Index
Preface
Preliminaries / Chapter 1:
Notations / 1.1:
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