Related papers: Integer-valued Polynomials, Pr\"ufer Domains and t…

Quadratic permutation polynomial interleavers over integer rings have recently received attention in practical turbo coding systems from deep space applications to mobile communications. In this correspondence, a necessary and sufficient…

The ring of integer-valued polynomials over a given subset $S$ of $\Z$ (or $ \mathrm{Int}(S,\Z ))$ is defined as the set of polynomials in $\Q[x]$ which maps $S$ to $\Z$. In factorization theory, it is crucial to check the irreducibility of…

If, for a subset S of Z^k, we compare the conditions of being parametrizable (a) by a single k-tuple of polynomials with integer coefficients, (b) by a single k-tuple of integer-valued polynomials and, (c) by finitely many k-tuples of…

In representation theory, the double centraliser property is an important property for a module (bimodule). It plays a fundamental role in many theories. In this paper, we extend this property to complexes in derived categories of finite…

In this paper we study the class of $w$-Jaffard domains in pullback constructions, and give new examples of these domains. In particular we give examples to show that the two classes of $w$-Jaffard and Jaffard domains are incomparable. As…

We estimate the frequency of singular matrices and of matrices of a given rank whose entries are parametrised by arbitrary polynomials over the integers and modulo a prime $p$. In particular, in the integer case, we improve a recent bound…

Let $F$ be a finite field of $char F > 3$ and $sl_{2}(F)$ be the Lie algebra of traceless $2\times 2$ matrices over $F$. This paper aims for the following goals: Find a basis for the $\mathbb{Z}_{2}$-graded identities of $sl_{2}(F)$; Find a…

In this paper, we introduce the notion of a $w$-Hilbert domain and investigate its basic properties. More precisely, we explore its relationship with Hilbert domains, strong Mori domains, and UMT domains by providing various examples using…

In this paper we consider the characteristic polynomial of not necessarily ranked posets. We do so by allowing the rank to be an arbitrary function from the poset to the nonnegative integers. We will prove two results showing that the…

In this paper, we exploit the r-Stirling numbers of both kinds in order to give explicit formulae for the values of the high order Bernoulli numbers and polynomials of both kinds at integers. We give also some identities linked the…

Let D be a Krull domain and Int(D) the ring of integer-valued polynomials on D. For any f in Int(D), we explicitly construct a divisor homomorphism from [f], the divisor-closed submonoid of Int(D) generated by f, to a finite sum of copies…

We introduce a notion of valued module which is suitable to study valued fields of positive characteristic. Then we built-up a robust theory of henselianity in the language of valued modules and prove Ax-Kochen Ershov type results.

Let $P_N(R)$ be the space of all real polynomials in $N$ variables with the usual inner product $<, >$ on it, given by integrating over the unit sphere. We start by deriving an explicit combinatorial formula for the bilinear form…

This paper is devoted to the study of independent spaces of q-polymatroids. With the aid of an auxiliary q-matroid it is shown that the collection of independent spaces satisfies the same properties as for q-matroids. However, in contrast…

Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extension problem reduces to a simple geometric obstruction on the…

Let $D$ be a commutative domain with field of fractions $K$, let $A$ be a torsion-free $D$-algebra, and let $B$ be the extension of $A$ to a $K$-algebra. The set of integer-valued polynomials on $A$ is ${\rm Int}(A) = \{f \in B[X] \mid f(A)…

Some integral properties of Jack polynomials, hypergeometric functions and invariant polynomials are studied for real normed division algebras.

This paper investigates the existence of integers that exclude two specific residence values modulo primes up to $p_k$ within the interval $[p_k^2, p_{k+1}^2]$. Using asymptotic results from analytic number theory, we establish bounds on…

We give formulas for the number of polynomials over a finite field with given root multiplicities, in particular in cases when the formula is surprisingly simple (a power of q). Besides this concrete interpretation, we also prove an…

In this article we shall study some basic properties of posynomial rings with particular emphasis on rings ${\rm Pos}(K,\mathbb{Q})[\bar x]$, and ${\rm Pos}(K,\mathbb{Z})[\bar x]$. The latter ring is the well known ring of Laurent…