Related papers: A solid angle polynomial with negative coefficient…
This paper has been withdrawn because the result turns out to be trivial.
Let $\vartheta(m)$ is number of nonzero coefficients in the $m$-th cyclotomic polynomial. For real $\gamma > 0$ and $x \ge 2$ we define $$H_{\gamma}(x)=\#\left\{m:~m=pq \le x, \ p<q\text{ primes }, \ \vartheta(m)\le m^{1/2+\gamma}\right\},…
We derive analytical expressions for the solid angle subtended by a right circular cylinder at a point source with cosine angular distribution in the case where the source and the cylinder axes are mutually orthogonal.
We provide explicit conditions for a real polynomial $f$ of degree 2d to be a sum of squares (s.o.s.), stated only in terms of the coefficients of $f$, i.e. with no lifting. All conditions are simple and provide an explicit description of a…
We classify here combinatorially rigid simple polytopes with three facets more than their dimension.
Article explicitly expresses Subgraph Isomorphism by a polynomial size asymmetric linear system.
This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.
Consider a polynomial of large degree n whose coefficients are independent, identically distributed, nondegenerate random variables having zero mean and finite moments of all orders. We show that such a polynomial has exactly k real zeros…
In the present paper we shall obtain a result on the image of polynomials with zero constant term on upper triangular matrix algebras over an algebraically closed field. This is a supplement to a result obtained by Panja and Prasad…
This note gives a simple approach to q-analogues of some results associated with Abel polynomials.
Abstract. We generalize the $b$-ary binomial coefficients with negative entries, which is based on the generating function obtained in early work. Besides an explicit expression involving the restricted partition, several properties such as…
In this paper, exact rate of decrease of best approximations of non-integer numbers by polynomials with integer coefficients of the growing exponentials is found on a disk in complex plane, on a cube in $\mathbb{R}^d$, and on a ball in…
The Koebe problem for univalent polynomials with real coefficients is fully solved only for trinomials, which means that in this case the Koebe radius and the extremal polynomial (extremizer) have been found. The general case remains open,…
Positively graded algebras are fairly natural objects which are arduous to be studied. In this article we query quotients of non-standard graded polynomial rings with combinatorial and commutative algebra methods.
A Littlewood polynomial is a single-variable polynomial all of whose coefficients lie in $\{ \pm 1\}$. We establish the leading term asymptotics of the number of reciprocal or skew-reciprocal Littlewood polynomials with square discriminant.…
The article is devoted to the investigation of transformation groups of polynomials over Cayley-Dickson algebras and their manifolds of zeros. The problems about expressibility of zeros with the help of roots and decomposibility of…
We investigate polynomials, called m-polynomials, whose generator polynomial has coefficients that can be arranged as a matrix, where q is a positive integer greater than one. Orthogonality relations are established and coefficients are…
In this paper, we obtain several new classes of irreducible polynomials having integer coefficients whose zeros lie inside an open disk around the origin or outside a closed annular region in the complex plane. Such irreducible polynomials…
We prove an inequality for polynomials applied in a symmetric way to non-commuting operators.
In this paper, we showed that the adjoint polynomial of a polyhedral cone equals the multidegree polynomial of the toric ideal with multigrading, both given by the vertex rays. This fact implies a conjecture of Aluffi, to the effect that…