scholarly journals On the lattice of polynomials with integer coefficients: successive minima in $L_2(0,1)$

2020 ◽  
Vol 124 (2) ◽  
pp. 109-128
Author(s):  
Wojciech Banaszczyk
Keyword(s):  
Integer Coefficients ◽  
Successive Minima

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

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.

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 Sampling methods for shortest vectors, closest vectors and successive minima

2009 ◽  
Vol 410 (18) ◽  
pp. 1648-1665 ◽  
Author(s):  
Johannes Blömer ◽  
Stefanie Naewe
Keyword(s):  
Sampling Methods ◽  
Successive Minima

scholarly journals An elementary proof of Minkowski's second inequality

1969 ◽  
Vol 10 (1-2) ◽  
pp. 177-181 ◽  
Author(s):  
I. Danicic
Keyword(s):  
Euclidean Space ◽  
Elementary Proof ◽  
Content Volume ◽  
Lattice Points ◽  
The Body ◽  
Dimensional Euclidean Space ◽  
Open Convex ◽  
Successive Minima ◽  
Linearly Independent ◽  
Independent Lattice

Let K be an open convex domain in n-dimensional Euclidean space, symmetric about the origin O, and of finite Jordan content (volume) V. With K are associated n positive constants λ1, λ2,…,λn, the ‘successive minima of K’ and n linearly independent lattice points (points with integer coordinates) P1, P2, …, Pn (not necessarily unique) such that all lattice points in the body λ,K are linearly dependent on P1, P2, …, Pj-1. The points P1,…, Pj lie in λK provided that λ > λj. For j = 1 this means that λ1K contains no lattice point other than the origin. Obviously

scholarly journals Counting Bounded Elements of a Number Field

2020 ◽  
Author(s):  
Mikołaj Fraczyk ◽  
Gergely Harcos ◽  
Péter Maga
Keyword(s):  
Group Theory ◽  
Number Field ◽  
Geometry Of Numbers ◽  
Combine Group ◽  
Successive Minima ◽  
Ideal Lattices ◽  
Linearly Independent ◽  
Ramification Theory

Abstract We estimate, in a number field, the number of elements and the maximal number of linearly independent elements, with prescribed bounds on their valuations. As a by-product, we obtain new bounds for the successive minima of ideal lattices. Our arguments combine group theory, ramification theory, and the geometry of numbers.

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