Related papers: New Multivariate Dimension Polynomials of Inversiv…
Shifted partial derivative (SPD) methods are a central algebraic tool for circuit lower bounds, measuring the dimension of spaces of shifted derivatives of a polynomial. We develop the Shifted Partial Derivative Polynomial (SPDP) framework,…
We use tools of additive combinatorics for the study of subvarieties defined by {\it high rank} families of polynomials in high dimensional $\mathbb{F} _q$-vector spaces. In the first, analytic part of the paper we prove a number properties…
We introduce the notion of the descent set polynomial as an alternative way of encoding the sizes of descent classes of permutations. Descent set polynomials exhibit interesting factorization patterns. We explore the question of when…
In this paper we generalize the classical Groebner basis technique to prove the existence and present a method of computation of a dimension polynomial in two variables associated with a finitely generated D-module, that is, a finitely…
Let $G\subset SO(4)$ denote a finite subgroup containing the Heisenberg group. In these notes we classify all these groups, we find the dimension of the spaces of $G$-invariant polynomials and we give equations for the generators whenever…
Invariants of generalized tensor fields on a line are classified using special polynomials P_mk^(-1/lambda) introduced here for this purpose. For the case of positive characteristic, a new invariant of formal power series, a width, is…
The work proves that, for three-dimensional upper triangular groups over a field of odd characteristic with an abelian unipotent subgroup, the ring of invariants is polynomial if and only if the unipotent subgroup is generated by…
The main purpose of this article is to introduce some new binomial difference sequence spaces of fractional order ${\tilde{\alpha}} $ along with infinite matrices. Some topological properties of these spaces are considered along with the…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
We define a transcendence degree for division algebras, by modifying the lower transcendence degree construction of Zhang. We show that this invariant has many of the desirable properties one would expect a noncommutative analogue of the…
We characterize the downsets of integer partitions (ordered by containment of Ferrers diagrams) and compositions (ordered by the generalized subword order) which have finite dimension in the sense of Dushnik and Miller. In the case of…
Having a large number of covariates can have a negative impact on the quality of causal effect estimation since confounding adjustment becomes unreliable when the number of covariates is large relative to the samples available. Propensity…
Polynomial inequalities lie at the heart of many mathematical disciplines. In this paper, we consider the fundamental computational task of automatically searching for proofs of polynomial inequalities. We adopt the framework of…
Here the polynomial interpolation approach is used to introduce the main results on multivariate normal algebraic systems. Next we bring a construction which shows that any standard algebraic system, with finite set of solutions, can be…
This article deals with three types of mutually inverse series relating Ferrers and associated Legendre functions of arbitrary complex indexes and orders established on the base of integral representations by using a number of generating…
In this article, we give an account of some recent irreducibility testing criteria for polynomials having integer coefficients over the field of rational numbers.
The notion of the weighted degree of a polynomial is a basic tool in Affine Algebraic Geometry. In this paper, we study the properties of the weighted multidegrees of polynomial automorphisms by a new approach which focuses on stable…
New criteria are shown that certain combinations of finite unimodal polynomials are unimodal. %Given unimodal polynomials with explicit expressions and dependent recursion relations, we propose an approach to determine their modes. As…
The ring of invariant polynomials ${\mathbb C}[V]^G$ over a given finite dimensional representation space $V$ of a complex reductive group $G$ is known, by a famous theorem of Hilbert, to be finitely generated. The general proof being…
Permutation trinomials over finite fields consititute an active research due to their simple algebraic form, additional extraordinary properties and their wide applications in many areas of science and engineering. In the present paper, six…