Related papers: A Note on Matching in Groups and Field Extensions
New criteria for which Cayley graphs of cyclic groups of any order can be completely determined--up to isomorphism--by the eigenvalues of their adjacency matrices is presented. Secondly, a new construction for pairs of nonisomorphic Cayley…
Ontologies have been used for the purpose of bringing system and consistency to subject and knowledge areas. We present a criticism of the present mathematical structure of ontologies and indicate that they are not sufficient in their…
The purpose of this article is to discuss recent advances in the growing field of phase retrieval, and to publicize open problems that we believe will be of interest to mathematicians in general, and algebraists in particular.
The purpose of this note is to explore some simple relations between loop measures, determinants, and Gaussian Markov fields.
The aim of this note is to give a geometric proof for classical local rigidity of lattices in semisimple Lie groups. We are reproving well known results in a more geometric (and hopefully clearer) way.
Consider the stable matching problem on two sets. We introduce the concept of a preference cycle and show how its natural presence in stable matchings proves a series of classical results in an elementary way.
We introduce a linearized version of group field theory. It can be viewed either as a group field theory over the additive group of a vector space or as an asymptotic expansion of any group field theory around the unit group element. We…
In this paper, we revisit the much studied problem of Pattern Matching with Swaps (Swap Matching problem, for short). We first present a graph-theoretic model, which opens a new and so far unexplored avenue to solve the problem. Then, using…
Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology-Based Query Answering. Entailment with existential rules is undecidable. We focus in this paper on conditions that ensure…
The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation…
We give a presentation of abelian class field theory.
The aim of this note is threefold: first, to present a few relevant facts about the way in which the technique of enriching contractive mappings was introduced; secondly, to expose the main contributions in the area of enriched mappings…
We formalize the general principle of significance with respect to binary relations which is a universal tool for description and analysis of various situations in and apart from mathematics. We derive the basic properties and focus on a…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
This note describes some open problems that can be examined with the purpose of gaining additional insight of how to solve the problem of finding a general classification of geodetic graphs
These are notes for a very rapid introduction to the basics of exterior differential systems and their connection with what is now known as Lie theory, together with some typical and not-so-typical applications to illustrate their use.
The purpose of this article is the study of the symmetries in a circular and linear harmonic oscillator chains system, and consequently use them as a means to find the eigenvalues of these configurations. Furthermore, a hidden…
Linear complementarity problems provide a powerful framework to model nonsmooth phenomena in a variety of real-world applications. In dynamical control systems, they appear coupled to a linear input-output system in the form of linear…
Arrangement theory plays an essential role in the study of the unfolding model used in many fields. This paper describes how arrangement theory can be usefully employed in solving the problems of counting (i) the number of admissible…
The aim of these notes is to provide a reasonably short and "hands-on" introduction to the differential calculus on associative algebras over a field of characteristic zero. Following a suggestion of Ginzburg's we call the resulting theory…