相关论文: On the arity gap of polynomial functions
We study the arity gap of functions of several variables defined on an arbitrary set A and valued in another set B. The arity gap of such a function is the minimum decrease in the number of essential variables when variables are identified.…
Let A and B be arbitrary sets with at least two elements. The arity gap of a function f: A^n \to B is the minimum decrease in its essential arity when essential arguments of f are identified. In this paper we study the arity gap of…
Given an $n$-ary $k-$valued function $f$, $gap(f)$ denotes the minimal number of essential variables in $f$ which become fictive when identifying any two distinct essential variables in $f$. We particularly solve a problem concerning the…
Abelian groups are classified by the existence of certain additive decompositions of group-valued functions of several variables with arity gap 2.
We investigate the Boolean functions with essential arity gap 2. We use Full Conjunctive Normal Forms instead of Zhegalkin's polynomials, which allow us to simplify the proofs and to obtain several combinatorial results, concerning the…
We characterize atypical values at infinity of a real polynomial function of three variables by a certain sum of indices of the gradient vector field of the function restricted to a sphere with a sufficiently large radius. This is an…
Given an $n$-ary $k-$valued function $f$, $gap(f)$ denotes the essential arity gap of $f$ which is the minimal number of essential variables in $f$ which become fictive when identifying any two distinct essential variables in $f$. In the…
The associativity property, usually defined for binary functions, can be generalized to functions of a given fixed arity n>=1 as well as to functions of multiple arities. In this paper, we investigate these two generalizations in the case…
In this technical report, certain interesting classification of arithmetical functions is proposed. The notion of additively decomposable and multiplicatively decomposable arithmetical functions is proposed. The concepts of arithmetical…
We consider the problem of defining polynomials over function fields of positive characteristic. Among other results, we show that the following assertions are true. 1. Let $\G_p$ be an algebraic extension of a field of $p$ elements and…
In this paper some classes of local polynomial functions on abelian groups are characterized by the properties of their variety. For this characterization we introduce a numerical quantity depending on the variety of the local polynomial…
In this paper, as an extension of the integer case, we define polynomial functions over the residue class rings of Dedekind domains, and then we give canonical representations and counting formulas for such polynomial functions. In…
The aim of this paper is to classify order-preserving functions according to their arity gap. Noteworthy examples of order-preserving functions are so-called aggregation functions. We first explicitly classify the Lov\'asz extensions of…
Inspired by a recent work of Mesnager, we present several new infinite families of quadratic ternary bent, near-bent and 2-plateaued functions from some known quadratic ternary bent functions. Meanwhile, the distribution of the Walsh…
We give a formula and an estimation for the number of irreducible polynomials in two (or more) variables over a finite field.
We introduce a new matroid (graph) invariant, the arboricity polynomial. Given a matroid, the arboricity polynomial enumerates the number of covers of the ground set by disjoint independent sets. We establish the polynomiality of the…
We extend to characteristic two recent results about isotropy of quadratic forms over function fields. In particular, we provide a characterization of function fields not only of quadratic forms but also more generally of polynomials in…
We provide upper bounds for the cardinality of the value set of a polynomial map in several variables over a finite field. These bounds generalize earlier bounds for univariate polynomials.
The article is devoted to approximate, global and along curves differentiability of functions over non-archimedean infinite fields with non-trivial valuations. Fields with zero and non-zero characteristics are considered. Spaces of…
The study of iterations of functions over a finite field and the corresponding functional graphs is a growing area of research with connections to cryptography. The behaviour of such iterations is frequently approximated by what is know as…