No cubic integer polynomial generates a Sidon sequence

2021 ◽  
Author(s):  
Artūras Dubickas ◽  
Aivaras Novikas
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

Integer Polynomial

2007 ◽  
Keyword(s):  
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
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