Related papers: Linked systems of symmetric group divisible design…
We study higher-degree generalizations of symplectic groupoids, referred to as {\em multisymplectic groupoids}. Recalling that Poisson structures may be viewed as infinitesimal counterparts of symplectic groupoids, we describe "higher''…
We present some of the group theoretic properties of reversing symmetry groups, and classify their structure in simple cases that occur frequently in several well-known groups of dynamical systems.
We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in C^n. Using the recent developments of Cauchy-Riemann geometry we provide the set of symmetries…
We study local normal forms for completely integrable systems on Poisson manifolds in the presence of additional symmetries. The symmetries that we consider are encoded in actions of compact Lie groups. The existence of Weinstein's…
A $configuration$ of a linkage $\Gamma$ is a possible positioning of $\Gamma$ in $\mathbb{R}^d$ and the collection of all such forms the configuration space $\mathcal{C}(\Gamma)$ of $\Gamma$. We here introduce the notion of the $symmetric…
We introduce a sub-symmetry of a differential system as an infinitesimal transformation of a subset of the system that leaves the subset invariant on the solution set of the entire system. We discuss the geometrical meaning and properties…
In recent years, the concepts of ``diversity'' and ``inclusion'' have attracted considerable attention across a range of fields, encompassing both social and biological disciplines. To fully understand these concepts, it is critical to not…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric linear and integer programs are studied from a group theoretical viewpoint. We show that for any linear program there exists an optimal solution…
Computational techniques for the construction of quasi-symmetric block designs are explored and applied to the case with $56$ points. One new $(56,16,18)$ and many new $(56,16,6)$ designs are discovered, and non-existence of $(56,12,9)$ and…
In this paper we construct two new infinite families of divisible design graphs based on symplectic graphs over rings with precisely three ideals.
The structure of the coincidence symmetry group of an arbitrary $n$-dimensional lattice in the $n$-dimensional Euclidean space is considered by describing a set of generators. Particular attention is given to the coincidence isometry…
Given a countable set of sites and a collection of flip rates at each site, we give a sufficient condition on the long-range dependancies of the flip rates ensuring the well-definedness of the corresponding spin system. This hypothesis has…
In this paper we introduce the notion of an idempotent system. This linear algebraic object is motivated by the structure of an association scheme. We focus on a family of idempotent systems, said to be symmetric. A symmetric idempotent…
We consider a class of systems of difference equations defined on an elementary quadrilateral of the ${\mathbb{Z}}^2$ lattice, define their eliminable and dynamical variables, and demonstrate their use. Using the existence of infinite…
In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…
An infinite family of nonschurian separable association schemes is constructed.
We examine the relation between supersymmetric lattice gauge theories constructed by the link approach and by orbifolding and show that they are equivalent. We discuss the number of preserved supersymmetries.
We give an attempt to build a classification of planar integral point sets. For two obtained classes, we provide general constructions of upper bounds for minimal diameter of integral point sets in higher dimensions of certain cardinality.…
We study the problem of determining whether a given temporal specification can be implemented by a symmetric system, i.e., a system composed from identical components. Symmetry is an important goal in the design of distributed systems,…
We study two kinds of generalizations of symmetric block designs to higher dimensions, the so-called $\mathcal{C}$-cubes and $\mathcal{P}$-cubes. For small parameters, all examples up to equivalence are determined by computer calculations.…