On the factorization of cyclic groups

  title={On the factorization of cyclic groups},
  author={N. D. Bruijn},
Rotations by roots of unity and Diophantine approximation
For a fixed integer n, we study the question whether at least one of the numbers $$\mathfrak {R}X\omega ^k$$RXωk, $$1\le k\le n$$1≤k≤n, is $$\varepsilon $$ε-close to an integer, for any possibleExpand
An Application of Cyclotomic Polynomial to Factorization of Finite Abelian Groups *
A finite abelian group G is said to have the Hajós-k-property (k>1) if from any decomposition of into a direct product of its subsets, it follows that one of these subsets is periodic, meaning thatExpand
Recent Progress on Favard Length Estimates for Planar Cantor Sets
The Favard length of a planar set E is the average length of its one-dimensional projections. If E is a purely unrectifiable self-similar set of Hausdorff dimension 1 in the plane, a theorem ofExpand
Recent progress on Favard length estimates for planar Cantor sets
This is an expository paper detailing some of the recent advances on the problem, with emphasis on the number-theoretic method developed in my paper with Bond and Volberg for rational product setsExpand
Buffon’s needle estimates for rational product Cantor sets
Let $S_\infty=A_\infty\times B_\infty$ be a self-similar product Cantor set in the complex plane, defined via $S_\infty=\bigcup_{j=1}^L T_j(S_\infty)$, where $T_j:\Bbb{C}\to\Bbb{C}$ have the formExpand
Tiling the integers with aperiodic tiles
A finite subset A of integers tiles the discrete line ℤ if the integers can be written as a disjoint union of translates of A. In some cases, necessary and sufficient conditions for A to tile theExpand
The Possibility of Extending Factorization Results to Infinite Abelian Groups
We shall consider three results on factoring finite abelian groups by subsets. These are the Hajós’, Rédei’s and simulation theorems. As L. Fuchs has done in the case of Hajós’ theorem we shallExpand
On Group Partitions Associated with Lower Bounds for Symmetric Ramsey Numbers
A detailed study of group partitions having this latter property is made, and the results of exhaustive searches for partitions of this type are reported which yield improved lower bounds for certain of these Ramsey numbers. Expand
An Integer Linear Programming Model for Tilings
An Integer Linear Model whose solutions are the aperiodic rhythms tiling with a given rhythm A can be used to efficiently check the necessity of the Coven-Meyerowitz’s pT2q condition and also to define an iterative algorithm that finds all the possible tilings of the rhythm A. Expand
Combinatorial and harmonic-analytic methods for integer tilings
A finite set of integers A tiles the integers by translations if Z can be covered by pairwise disjoint translated copies of A. In this article, we develop concepts and methods that enable aExpand


On bases for the set of integers
• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official publishedExpand