A multivariate polynomial P (x 1 , . . . , xn) with real coefficients is said to be absolutely positive from a real number B iff it and all of its non-zero partial derivatives of every order are positive for x 1 , . . . , xn β₯ B. We call such B a bound for the absolute positiveness of P . This paper
Bounds for the Roots of Lacunary Polynomials
β Scribed by Maurice Mignotte
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 200 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0747-7171
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β¦ Synopsis
We give bounds for the roots of such polynomials with complex coefficients. These bounds are much smaller than for general polynomials.
π SIMILAR VOLUMES
It is proved that the chromatic polynomial of a connected graph with n vertices and m edges has a root with modulus at least (m&1)Γ(n&2); this bound is best possible for trees and 2-trees (only). It is also proved that the chromatic polynomial of a graph with few triangles that is not a forest has a
## Abstract We examine some properties of the 2βvariable greedoid polynomial __f__(__GΒ·,t,z__) when __G__ is the branching greedoid associated to a rooted graph or a rooted directed graph. For rooted digraphs, we show a factoring property of __f__(__GΒ·,t,z__) determines whether or not the rooted di
Let K be an algebraic number field such that all the embeddings of K into C are real. We denote by O K the ring of algebraic integers of K. Let F(X, Y) be an irreducible polynomial in K[X, Y ]&K[Y ] of total degree N and of degree n>0 in Y. We denote by F N (X, Y ) its leading homogeneous part. Supp