Related papers: A local-global principle for linear dependence of …

In this paper we prove a characterization of continuity for polynomials on a normed space. Namely, we prove that a polynomial is continuous if and only if it maps compact sets into compact sets. We also provide a partial answer to the…

This paper investigates equivalence of square multivariate polynomial matrices with the determinant being some power of a univariate irreducible polynomial. We first generalized a global-local theorem of Vaserstein. Then we proved these…

For some Maltsev conditions $\Sigma$ it is enough to check if a finite algebra $\mathbf A$ satisfies $\Sigma$ locally on subsets of bounded size, in order to decide, whether $\mathbf A$ satisfies $\Sigma$ (globally). This local-global…

A linearized polynomial $f(x)\in\mathbb F_{q^n}[x]$ is called scattered if for any $y,z\in\mathbb F_{q^n}$, the condition $zf(y)-yf(z)=0$ implies that $y$ and $z$ are $\mathbb F_{q}$-linearly dependent. In this paper two generalizations of…

We introduce linear holonomy on Poisson manifolds. The linear holonomy of a Poisson structure generalizes the linearized holonomy on a regular symplectic foliation. However, for singular Poisson structures the linear holonomy is defined for…

We give a criterion whether given Eisenstein polynomials over a local field K define the same extension over K in terms of a certain non-Archimedean metric on the set of polynomials. The criterion and its proof depend on ramification…

We call shifted power a polynomial of the form $(x-a)^e$. The main goal of this paper is to obtain broadly applicable criteria ensuring that the elements of a finite family $F$ of shifted powers are linearly independent or, failing that, to…

We describe a multivariable polynomial invariant for certain class of non isolated hypersurface singularities generalizing the characteristic polynomial on monodromy. The starting point is an extension of a theorem due to Le Dung Trang and…

We develop a rigorous theory of non-local Hamiltonian structures, built on the notion of a non-local Poisson vertex algebra. As an application, we find conditions that guarantee applicability of the Lenard-Magri scheme of integrability to a…

In this paper local polynomials on Abelian groups are characterized by a "local" Fr\'echet-type functional equation. We apply our result to generalize Montel's Theorem and to obtain Montel-type theorems on commutative groups.

We consider three classification systems for distributed decision tasks: With unbounded computation and certificates, defined by Balliu, D'Angelo, Fraigniaud, and Olivetti [JCSS'18], and with (two flavors of) polynomially bounded local…

In the local, characteristic 0, non archimedean case, we consider distributions on GL(n+1) which are invariant under the adjoint action of GL(n). We prove that such distributions are invariant by transposition. This implies that an…

Let $G$ be a Lie group and $\Gamma$ be a lattice in $G$. We introduce the notion of locally unipotent invariant measures on $G/\Gamma$. We then prove that under some conditions, the limit measure supported on the image of polynomial…

The interaction between local traits and global frameworks of mathematical objects has long endured as a central theme in various mathematical domains. A graph \(G\) is referred to as locally linear provided that the subgraph induced by the…

Reliability of a system is considered where the components' random lifetimes may be dependent. The structure of the system is described by an associated "lattice polynomial" function. Based on that descriptor, general framework formulas are…

In this paper, we study the isotropy groups of locally finite derivations of the polynomial ring $\mathbb{K}[X,Y]$, using Van den Essen's classification of locally finite derivations in two variables. We compare the isotropy group of a…

Let $K$ be a number field, $f\in K[x]$ a quadratic polynomial, and $n\in\{1,2,3\}$. We show that if $f$ has a point of period $n$ in every non-archimedean completion of $K$, then $f$ has a point of period $n$ in $K$. For $n\in\{4,5\}$ we…

We consider certain functional identities on the matrix algebra $M_n$ that are defined similarly as the trace identities, except that the "coefficients" are arbitrary polynomials, not necessarily those expressible by the traces. The main…

From around 2010 onward, Elsner et al.,developed and applied a method in which the algebraic independence of n quantities x_1,...,x_n over a field is transferred to further n quantities y_1,...,y_n by means of a system of polynomials in 2n…

We resolve affirmatively some conjectures of Reiner, Stanton, and White \cite{ReinerComm} regarding enumeration of transportation matrices which are invariant under certain cyclic row and column rotations. Our results are phrased in terms…