Related papers: On common energies and sumsets

In this note we show a simple formula for the coefficients of the polynomial associated with the sums of powers of the terms of an arbitrary arithmetic progression. This formula consists of a double sum involving only ordinary binomial…

Let f be a real or complex polynomial. We give an algorithm to compute the set of generalized critical values. The algorithm uses a finite dimensional space of rational arcs along which we can reach all generalized critical values of f.

Two fundamental questions in the theory of Groebner bases are decision ("Is a basis G of a polynomial ideal a Groebner basis?") and transformation ("If it is not, how do we transform it into a Groebner basis?") This paper considers the…

We give a short proof of polynomial recurrence with large intersection for additive actions of finite-dimensional vector spaces over countable fields on probability spaces, improving upon the known size and structure of the set of strong…

A general theorem on fibers of singular sets is presented.

We present combinatorial rules (one theorem and two conjectures) concerning three bases of Z[x1,x2,....]. First, we prove a "splitting" rule for the basis of key polynomials [Demazure '74], thereby establishing a new positivity theorem…

In this note, we study substructures of generalised power series fields induced by families of well-ordered subsets of the group of exponents. We characterise the set-theoretic and algebraic properties of the induced substructures in terms…

In this paper, we derive some interesting symmetric properties for the geenralized Euler numbers and polynomials.

In a cluster algebra, a subset of initial cluster variables can be specialised in such a way that all elements of the resulting algebra become polynomial in the remaining variables.

Two of the pillars of combinatorics are the notion of choosing an arbitrary subset of a set with $n$ elements (which can be done in $2^n$ ways), and the notion of choosing a $k$-element subset of a set with $n$ elements (which can be done…

Using Newton polygons, a key factorization result for polynomials over discrete valuation domains is proved, which in particular yields new irreducibility criteria including a generalization of the classical irreducibility criterion of…

The A-hierarchy is a parametric analogue of the polynomial hierarchy in the context of paramterised complexity theory. We give a new characterisation of the A-hierarchy in terms of a generalisation of the SUBSET-SUM problem.

This is the second part of a work dedicated to the study of Bernstein-Sato polynomials for several analytic functions depending on parameters. In this part, we give constructive results generalizing previous ones obtained by the author in…

The main goal of this paper is to generalize Bohr's phenomenon from complex one-dimensional analysis to higher dimensions in the framework of Quaternionic Analysis.

Exponential distributions appear in a wide range of applications including chemistry, nuclear physics, time series analyses, and stock market trends. There are conceivable circumstances in which one would be interested in the cumulative…

There are two different notions for symbolic powers of ideals existing in the literature, one defined in terms of associated primes, the other in terms of minimal primes. Elaborating on an idea known to Eisenbud, Herzog, Hibi, and Trung, we…

The characteristic polynomial for a chain of dipole-dipole coupled two-level atoms with nearest-neighbour and next-nearest-neighbour interactions is developed for the study of eigenvalues and eigenvectors for single-photon excitations. We…

In this paper, we provide a necessary and sufficient condition ensuring the property of exponential dichotomy for periodic linear systems of generalized differential equations. This condition allow us to revisit a recent result of…

A new polynomial sieve is presented and used to show that almost all integers have at most one representation as a sum of two values of a given polynomial of degree at least 3.

In this paper, we prove normality criteria for families of meromorphic functions involving sharing of a holomorphic function by a certain class of differential polynomials. Results in this paper extends the works of different authors…