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 Mahler measures of polynomials that are sums of a bounded number of monomials

2016 ◽  
Vol 13 (06) ◽  
pp. 1603-1610 ◽  
Author(s):  
Edward Dobrowolski ◽  
Chris Smyth
Keyword(s):  
Real Line ◽  
Closed Subset ◽  
Final Section ◽  
Mahler Measure ◽  
Laurent Polynomials ◽  
Integer Coefficients ◽  
Bounded Number ◽  
Integer Polynomial ◽  
Isolated Point

We study Laurent polynomials in any number of variables that are sums of at most [Formula: see text] monomials. We first show that the Mahler measure of such a polynomial is at least [Formula: see text], where [Formula: see text] is the height of the polynomial. Next, restricting to such polynomials having integer coefficients, we show that the set of logarithmic Mahler measures of the elements of this restricted set is a closed subset of the nonnegative real line, with [Formula: see text] being an isolated point of the set. In the final section, we discuss the extent to which such an integer polynomial of Mahler measure [Formula: see text] is determined by its [Formula: see text] coefficients.

Irreducibility Results for Compositions of Polynomials with Integer Coefficients

2006 ◽  
Vol 149 (1) ◽  
pp. 31-41 ◽  
Author(s):  
Anca Iuliana Bonciocat ◽  
Alexandru Zaharescu
Keyword(s):  
Integer Coefficients

Transitive polynomial transformations of residue class rings

2002 ◽  
Vol 12 (2) ◽  
Author(s):  
M.V. Larin
Keyword(s):  
Residue Class ◽  
Integer Coefficients ◽  
Polynomial Transformations

AbstractWe give a complete description of the polynomials f(x) with integer coefficients such that the period of the recurring sequence u

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

scholarly journals Counting polynomial subset sums

2018 ◽  
Vol 47 (1) ◽  
pp. 67-84 ◽  
Author(s):  
Jiyou Li ◽  
Daqing Wan
Keyword(s):  
Subset Sums ◽  
Counting Polynomial
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