Related papers: Totally Symmetric Sets

This paper introduces a SAT-based technique that calculates a compact and complete symmetry-break for finite model finding, with the focus on structures with a single binary operation (magmas). Classes of algebraic structures are typically…

We investigate geometric properties of homogeneous parabolic geometries with generalized symmetries. We show that they can be reduced to a simpler geometric structures and interpret them explicitly. For specific types of parabolic…

The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric integer programs are studied from a group theoretical viewpoint. We investigate the structure of integer solutions of integer programs and show…

A metric space is said to be all-set-homogeneous if any of its partial isometries can be extended to a genuine isometry. We give a classification of a certain subclass of all-set-homogeneous length spaces.

We investigate in detail a homomorphism which we call the 2-Selmer signature map from the $2$-Selmer group of a number field $K$ to a nondegenerate symmetric space, in particular proving the image is a maximal totally isotropic subspace.…

We define and study homotopy groups of cubical sets. To this end, we give four definitions of homotopy groups of a cubical set, prove that they are equivalent, and further that they agree with their topological analogues via the geometric…

For suitable subgroups of a finitely generated group, we define the intersection number of one subgroup with another subgroup and show that this number is symmetric. We also give an interpretation of this number.

This paper is a survey of some properties of the braid groups and related groups that lead to questions on mapping class groups.

We define the notion of extrinsic symplectic symmetric spaces and exhibit some of their properties. We construct large families of examples and show how they fit in the perspective of a complete classification of these manifolds. We also…

We study the concept of universal sets from the additive--combinatorial point of view. Among other results we obtain some applications of this type of uniformity to sets avoiding solutions to linear equations, and get an optimal upper bound…

Homomorphically full graphs are those for which every homomorphic image is isomorphic to a subgraph. We extend the definition of homomorphically full to oriented graphs in two different ways. For the first of these, we show that…

Lie symmetry group method is applied to study the Born-Infeld equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra…

Due to their elegant and simple nature, unitary Cayley graphs have been an active research topic in the literature. These graphs are naturally connected to several branches of mathematics, including number theory, finite algebra,…

One applies the symmetry group theory for study the partial differential equations of Tzitzeica surfaces theory. One finds infinitesimal symmetries, Lagrangians and a new solution of Titzeica equation.

Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…

This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the K\"ahler class, is used to define and characterize a special class…

We construct classifying spaces for discrete and compact Lie groups, with the property that they are topological groups and complete metric spaces in a natural way. We sketch a program in view of extending these constructions.

In these notes the exact renormalization group formulation of the scalar theory is briefly reviewed. This regularization scheme is then applied to supersymmetric theories. In case of a supersymmetric gauge theory it is also shown how to…

We look at the supersymmetric generalization of harmonic maps into Lie groups, known to physicists as the chiral model. Explicit solutions to the equations are found and examined using Backlund transformations.

The symmetric group acts on the power set and also on the set of square free polynomials. These two related representations are analyzed from the stability point of view. An application is given for the action of the symmetric group on the…