Related papers: Pure O-sequences: known results, applications, and…
The goal of this paper is to present an algebraic approach to the basic results of the theory of linear recurrence relations. This approach is based on the ideas from the theory of representations of one endomorphisms (a special case of…
This work is a study of polynomial compositions having a fixed number of terms. We outline a recursive method to describe these characterizations, give some particular results and discuss the general case. In the final sections, some…
Experimental mathematics is an experimental approach to mathematics in which programming and symbolic computation are used to investigate mathematical objects, identify properties and patterns, discover facts and formulas and even…
Necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a 3-connected simple graph are detailed. Conditions are also given under which such a sequence is necessarily 3-connected i.e. the sequence…
We introduce anyonic Lie algebras in terms of structure constants. We provide the simplest examples and formulate some open problems.
The paper considers urn schemes in which several urns can be involved. Simplified formulas are proposed that allow direct calculation of probabilities without the use of elements combinatorics.
After recalling the notion of Lie algebroid, we construct these structures associated with contact forms or systems. We are then interested in particular classes of Lie Rinehart algebras.
We prove that if a standard determinantal scheme is level, then its h-vector is a log-concave pure O-sequence, and conjecture that the converse also holds. Among other cases, we prove the conjecture in codimension two, or when the entries…
We briefly review superstring theories, highlighting the important concepts, developments, and open problems of the subject.
Algebraic statistics uses tools from algebra (especially from multilinear algebra, commutative algebra and computational algebra), geometry and combinatorics to provide insight into knotty problems in mathematical statistics. In this survey…
This expository paper starts with a brief survey on the relation between partitions and surjections of sets, and then gives a quick introduction to the theories of incidence algebras, Segal groupoids and combinatorial species. The aim is to…
The book gives a detailed exposition of basic concepts and results of a theory of processes. The presentation of theoretical concepts and results is accompanied with illustrations of their application to solving various problems of…
What is Sequence Algebra? This is a question that any teacher or student of mathematics or computer science can engage with. Sequences are in Calculus, Combinatorics, Statistics and Computation. They are foundational, a step up from number…
This paper considers some open questions related to the inverse problem of pure point diffraction, in particular, what types of objects may diffract, and which of these may exhibit the same diffraction. Some diverse objects with the same…
In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.
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.
In many applications of the probabilistic method, one looks to study phenomena that occur ``with high probability''. More recently however, in an attempt to understand some of the most fundamental problems in combinatorics, researchers have…
A few of the algebraic and topological properties of int. fuzzy continuity and int. fuzzy uniform continuity are investigated. Also, the concept of int. fuzzy uniform convergence is introduced thereafter a few result on int. fuzzy uniform…
Motivated by the remarkable interplay between (chordal) graphs and matrix algebra, we associate to each graph a so-called completion number that might encode some aspects of that interplay. We show that this number is not trivial, and we…
We prove that the existence of finite combinatorial objects such as affine planes, mutually orthogonal Latin squares, and resolvable balanced incomplete block designs can be reformulated as the existence of certain algorithmic reductions…