Article

Schützenberger groups ofH-classes in the semigroup of all binary relations on a set

December 1973
Semigroup Forum 6(1)

DOI:10.1007/BF02389130

Authors:

In a recent paper [1972], R. L. Brandon, D. W. Hardy, and G. Markowsky, showed that the Schützenberger group Γ(H) of anH-class H inB X is isomorphic to the automorphism group of a lattice V associated with H. For H a group this result is due to K.A. Zaretskiî [1963]. In this note we show that a small modification of Zaretskiî's method for H a group simultaneously gives the result of Brandon, Hardy and Markowsky.

ResearchGate has not been able to resolve any citations for this publication.

The Schützenberger group of an H -class in the semigroup of binary relations

Article

Full-text available

Jan 1972

K. A. Zaretskii has associated a lattice V(α) with each binary relation α, and he has shown that Hα is isomorphic with the group of all automorphisms of V(α) if Hα is a group. This result is extended in this paper by showing that for any binary relation α, the Schützenberger group Γ (Hα) is isomorphic with the group of all automorphisms of V(α).

Полугруппа бинарных отношений. (The semigroup of binary relations)

Jan 1963
291

K A Zaretskiî
K.A. Zaretskiî

Article

Automorphism groups of posets with forbidden subposets

August 1992 · Discrete Mathematics

Gerhard Behrendt

We show that there exists a finite set S of finite posets such that the following holds. Whenever, (Y,⩽) is not isomorphic to a member of S and it is not trivially ordered then for every finite group G there exists a finite poset (X,⩽) which has no induced subposet isomorphic to (Y,⩽) such that G is isomorphic to the automorphism group of (X,⩽). For some members (Y,⩽) of S we give necessary and ... [Show full abstract] sufficient conditions for a group G to be isomorphic to the automorphism group of a finite poset (X,⩽) which has no induced subposet (Y,⩽). This includes the classification of the automorphism groups of finite interval orders and series- parallel posets.

Article

Quasi-rigidity of hyperbolic 3-manifolds and scattering theory

April 1996 · Duke Mathematical Journal

Take two isomorphic convex co-compact co-infinite volume Kleinian groups, whose regular sets are diffeomorphic. The quotient of hyperbolic 3-space by these groups gives two hyperbolic 3-manifolds whose scattering operators may be compared. We prove that the operator norm of the difference between the scattering operators is small, then the groups are related by a coorespondingly small ... [Show full abstract] quasi-conformal deformation. This in turn implies that the two hyperbolic 3-manifolds are quasi-isometric.

Article

Full-text available

Recognition of Unigraphs through Superposition of Graphs

January 2011 · Journal of Graph Algorithms and Applications

Unigraphs are graphs uniquely determined by their own degree sequence up to isomorphism. In this paper a structural description for unigraphs is introduced: vertex set is partitioned into three disjoint sets while edge set is divided into two different classes. This characterization allows us to design a new linear time recognition algorithm that works recursively pruning the degree sequence of ... [Show full abstract] the graph. The algorithm detects two particular graphs whose superposition generates the given unigraph.

Article

Two-sided Configuration of Polycyclic Groups and Isomorphism

November 2015

The concept of configuration was first introduced to give a condition for the amenability of groups. Then the concept of two-sided configuration was suggested to provide " normality " to study the group structures more efficiently. We show that if G and H have the same two-sided configuration sets and N is a normal subgroup of G with polycyclic quotient, then there is a normal subgroup N of H ... [Show full abstract] such that G/N ∼ = H/N. Using two-sided configuration equivalence, we prove that being two-sided configuration equivalent to a group G which has a normal sub-series, each of its factor is polycyclic, leads to isomorphism. To show this, we first prove the statement for polycyclic groups. In particular, for the class of nilpotent, FC, the notions of two-sided configuration equivalence and isomorphism are coincided.

Article

Investigation of phase diagram of hard-core boson model with non-ergodic contributions

January 2009 · Journal of Physical Studies

The hard-core boson model which is isomorph to the XXZ anisotropic Heisnberg model is investigated in the self-consistent field approach. The Helmholtz free energy, the set of self-consistency equations and the pseudospin Green's functions are obtained. The approach used corresponds to random phase approximation with the inclusion of non-ergodic contributions. Their influence on the shape of ... [Show full abstract] phase diagram and position of the phase transition lines is analysed.

Article

Wings and perfect graphs

March 1990 · Discrete Mathematics

Stephan Olariu

An edge uv of a graph G is called a wing if there exists a chordless path with vertices u, v, x, y and edges uv, vx, xy. The wing-graph W(G) of a graph G is a graph having the same vertex set as G; uv is an edge in W(G) if and only if uv is a wing in G. A graph G is saturated if G is isomorphic to W(G). A star-cutset in a graph G is a non-empty set of vertices such that G — C is disconnected and ... [Show full abstract] some vertex in C is adjacent to all the remaining vertices in C. V. Chvátal proposed to call a graph unbreakable if neither G nor its complement contain a star-cutset. We establish several properties of unbreakable graphs using the notions of wings and saturation. In particular, we obtain seven equivalent versions of the Strong Perfect Graph Conjecture.

Article

Graphs determined by their finite induced subgraphs

October 1986 · Journal of Combinatorial Theory Series B

Dugald Macpherson

A classification is given of those countable graphs which are determined up to isomorphism by the set of their finite induced subgraphs.

Article

Filtrations of meromorphic ℂ * actions on complex manifolds

December 1983 · MATHEMATICA SCANDINAVICA

Article

Some order dualities in logic, games and choices

February 2007 · International Game Theory Review

Bernard Monjardet

We first present the concept of duality appearing in order theory, i.e. the notions of dual isomorphism and of Galois connection. Then, we describe two fundamental dualities, the duality extension/intention associated with a binary relation between two sets, and the duality between implicational systems and closure systems. Finally, we present two "concrete" dualities occuring in social choice ... [Show full abstract] and in choice functions theories.

Article

Commutative algebras and representations of the category of finite sets

November 2010 · Journal of Mathematical Sciences

S. S. Podkorytov

We prove that two finite-dimensional commutative algebras over an algebraically closed field are isomorphic if and only if they give rise to isomorphic representations of the category of finite sets and surjective maps.

Article

Meet- and join-irreducibility of additive hereditary properties of graphs

May 2002 · Discrete Mathematics

An additive hereditary property of graphs is any class of simple graphs which is closed under unions, subgraphs and isomorphisms. The set of all such properties is a lattice with set inclusion as the partial ordering. We study the elements of this lattice which are meet- join- and doubly-irreducible. The significance of these elements for the lattice of ideals of this lattice is discussed.

Article

Unit-distance graphs, graphs on the integer lattice and a Ramsey type result

February 1996 · Aequationes mathematicae

Let (R 2, 1) denote the graph withR 2 as the vertex set and two vertices adjacent if and only if their Euclidean distance is 1. The problem of determining the chromatic numberÖ2\sqrt 2 ) denote a graph with vertex setZ 2 and two vertices adjacent if and only if their Euclidean distance is in the closed interval [r – Ö2\sqrt 2 ,r + Ö2\sqrt 2 ]. A simple graph is faithfully Ö2\sqrt 2 -recurring ... [Show full abstract] inZ 2 if there exists a real numberd > 0 such that, for arbitrarily larger, G is isomorphic to a subgraph of (Z 2,r, Ö2\sqrt 2 ) in which every pair of vertices are at least distancedr apart. Chilakamarri has shown that, ifG is a finite simple graph, thenG is isomorphic to a subgraph of (R 2, 1) if and only ifG is faithfully Ö2\sqrt 2 -recurring inZ 2. In this paper we prove thatÖ2\sqrt 2 ) Ö2\sqrt 2 ,r + Ö2\sqrt 2 ] or there exists a set of three vertices closest to each other with three distinct colors.