Integer Polynomial

2007 ◽  
Keyword(s):  
Integer Polynomial

scholarly journals Orbit Polynomial of Graphs versus Polynomial with Integer Coefficients

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 710
Author(s):  
Modjtaba Ghorbani ◽  
Maryam Jalali-Rad ◽  
Matthias Dehmer
Keyword(s):  
Integer Coefficients ◽  
Integer Polynomial ◽  
Counting Polynomial

Suppose ai indicates the number of orbits of size i in graph G. A new counting polynomial, namely an orbit polynomial, is defined as OG(x) = ∑i aixi. Its modified version is obtained by subtracting the orbit polynomial from 1. In the present paper, we studied the conditions under which an integer polynomial can arise as an orbit polynomial of a graph. Additionally, we surveyed graphs with a small number of orbits and characterized several classes of graphs with respect to their orbit polynomials.

scholarly journals Integer Polynomial Optimization in Fixed Dimension

2006 ◽  
Vol 31 (1) ◽  
pp. 147-153 ◽  
Author(s):  
Jesús A. De Loera ◽  
Raymond Hemmecke ◽  
Matthias Köppe ◽  
Robert Weismantel
Keyword(s):  
Polynomial Optimization ◽  
Fixed Dimension ◽  
Integer Polynomial

POLYNOMIAL ROOT SEPARATION

2010 ◽  
Vol 06 (03) ◽  
pp. 587-602 ◽  
Author(s):  
YANN BUGEAUD ◽  
MAURICE MIGNOTTE
Keyword(s):  
Integer Polynomials ◽  
Integer Polynomial

We discuss the following question: How close to each other can two distinct roots of an integer polynomial be? We summarize what is presently known on this and related problems, and establish several new results on root separation of monic, integer polynomials.

scholarly journals Mixed integer polynomial programming

2015 ◽  
Vol 72 ◽  
pp. 387-394 ◽  
Author(s):  
Vivek Dua
Keyword(s):  
Mixed Integer ◽  
Polynomial Programming ◽  
Integer Polynomial

ROOTS OF POLYNOMIALS WITH DOMINANT TERM

2011 ◽  
Vol 07 (05) ◽  
pp. 1217-1228 ◽  
Author(s):  
ARTŪRAS DUBICKAS
Keyword(s):  
Constant Coefficient ◽  
Roots Of Unity ◽  
Algebraic Numbers ◽  
Algebraic Integers ◽  
Dominant Term ◽  
Minimal Weight ◽  
Number Systems ◽  
Integer Polynomials ◽  
Roots Of Polynomials ◽  
Integer Polynomial

We characterize all algebraic numbers which are roots of integer polynomials with a coefficient whose modulus is greater than or equal to the sum of moduli of all the remaining coefficients. It turns out that these numbers are zero, roots of unity and those algebraic numbers β whose conjugates over ℚ (including β itself) do not lie on the circle |z| = 1. We also describe all algebraic integers with norm B which are roots of an integer polynomial with constant coefficient B and the sum of moduli of all other coefficients at most |B|. In contrast to the above, the set of such algebraic integers is "quite small". These results are motivated by a recent paper of Frougny and Steiner on the so-called minimal weight β-expansions and are also related to some work on canonical number systems and tilings.

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