Related papers: Algebraic and geometric methods in enumerative com…

In this paper we explore the possibility of using computational algebraic methods to analyze a class of consensus protocols. We state some necessary conditions for convergence under consensus protocols that are polynomials.

These notes follow my articles [1, 6], and give some new important details. We propose here a new combinatorial method of encoding of measure spaces with measure preserving transformations, (or groups of transformations) in order to give…

Enveloping algebras of Hom-Lie and Hom-Leibniz algebras are constructed.

A new method of algebraic nature is proposed for the study of the asymptotic properties of special polynomials. The technique we foresee is based on the use of umbral operators, allowing a unified treatment of a large body of polynomial…

We give a complete geometrical description of the effective Hamiltonians common in nuclear shell model calculations. By recasting the theory in a manifestly geometric form, we reinterpret and clarify several points. Some of these results…

The paper suggests a short survey of integration algorithms which evolved since 1982. These theorems and algorithms form discrete versions of the calculus theorems.

This is a survey article on classical groups (over arbitrary division rings) and their geometries.

In this paper, we give a survey of a geometrical theory of Jacobi forms of higher degree. And we present some geometric results and discuss some geometric problems to be investigated in the future.

This document presents a combinatorial framework for analyzing assembly systems using generating functions. We explore the theory through concrete examples, such as linear polymers, and develop recursive equations to characterize valid…

We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based…

We give a short introduction to the methods of representing polynomial and trigonometric series that are often used in Celestial Mechanics. A few applications are also illustrated.

Various applications of quantum algebraic techniques in nuclear structure physics and molecular physics are briefly reviewed. Contains 81 references.

We demonstrate the use of several tools from Algebraic Combinatorics such as Young tableaux, symmetry operators, the Littlewood-Richardson rule and discrete Fourier transforms of symmetric groups in investigations of algebraic curvature…

In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…

Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we review the development and theory of symplectic…

A general framework for obtaining certain types of contracted and centrally extended algebras is presented. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.

There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.

Symmetric functions provide one of the most efficient tools for combinatorial enumeration, in the context of objects that may be acted upon by permutations. Only assuming a basic knowledge of linear algebra, we introduce and describe the…

This paper is a survey of computational issues in algebraic geometry, with particular attention to the theory of Grobner bases and the regularity of an algebraic variety. 1. A geometric introduction to Grobner bases. 2. An algebraic…

The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology,…