Notes on the Roots of Steiner Polynomials
نویسنده
چکیده
We study the location and the size of the roots of Steiner polynomials of convex bodies in the Minkowski relative geometry. Based on a problem of Teissier on the intersection numbers of Cartier divisors of compact algebraic varieties it was conjectured that these roots have certain geometric properties related to the inand circumradius of the convex body. We show that the roots of 1-tangential bodies fulfill the conjecture, but we also present convex bodies violating each of the conjectured properties.
منابع مشابه
On the Location of Roots of Steiner Polynomials
We investigate the roots of relative Steiner polynomials of convex bodies. In dimension 3 we give a precise description of their location in the complex plane and we study the analogous problem in higher dimensions. In particular, we show that the roots (in the upper half plane) form a convex cone; for dimensions ≤ 9 this cone is completely contained in the (open) left half plane, which is not ...
متن کاملOn Classifications of Random Polynomials
Let $ a_0 (omega), a_1 (omega), a_2 (omega), dots, a_n (omega)$ be a sequence of independent random variables defined on a fixed probability space $(Omega, Pr, A)$. There are many known results for the expected number of real zeros of a polynomial $ a_0 (omega) psi_0(x)+ a_1 (omega)psi_1 (x)+, a_2 (omega)psi_2 (x)+...
متن کاملRecursive Constructions of N-polynomials over GF (2s)
This paper presents procedures for constructing irreducible polynomials over GF(2s ) with linearly independent roots (or normal polynomials or N-polynomials). For a suitably chosen initial N-polynomial F0(x) ∈ GF(2s ) of degree n, polynomials Fk(x) ∈ GF(2s ) of degrees n2k are constructed by iteratively applying the transformation x → x + x−1, and their roots are shown to form a normal basis of...
متن کاملIntrinsic Volumes and Successive Radii
Motivated by a problem of Teissier to bound the intrinsic volumes of a convex body in terms of the inradius and the circumradius of the body, we give upper and lower bounds for the intrinsic volumes of a convex body in terms of the elementary symmetric functions of the so called successive inner and outer radii. These results improve on former bounds and, in particular, they also provide bounds...
متن کاملOn the Roots of Hosoya Polynomial of a Graph
Let G = (V, E) be a simple graph. Hosoya polynomial of G is d(u,v) H(G, x) = {u,v}V(G)x , where, d(u ,v) denotes the distance between vertices u and v. As is the case with other graph polynomials, such as chromatic, independence and domination polynomial, it is natural to study the roots of Hosoya polynomial of a graph. In this paper we study the roots of Hosoya polynomials of some specific g...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007