A non-analytic proof of the Newman-Znám result for disjoint covering systems
type: Item
instance of: scholarly article
title: A non-analytic proof of the Newman-Znám result for disjoint covering systems
zbMATH Open document ID: 0608.10006
DOI: 10.1007/BF02579384
author: Marc A. Berger
author: Alexander Felzenbaum
author: Aviezri S. Fraenkel
published in: Combinatorica
publication date: 1986-01-01T00:00:00Z
review text: A disjoint covering system is a partition of the set of all integers into a finite number of residue classes. The authors developed recently an elementary lattice parallelotopes technique which avoids the use of complex numbers in proofs of some results concerning disjoint covering systems. In the paper they use this technique to give the first combinatorial proof of a generalization of the well known result that the largest modulus N of a residue class in a disjoint covering system appears at least p times in the system, where p is the smallest prime divisor of N.
Mathematics Subject Classification ID: 11A07
Mathematics Subject Classification ID: 11H31
Mathematics Subject Classification ID: 51A15
Mathematics Subject Classification ID: 11B25
Mathematics Subject Classification ID: 05B40
zbMATH DE Number: 3983253
zbMATH Keywords: maximal modulus
zbMATH Keywords: arithmetic progression
zbMATH Keywords: disjoint covering system
zbMATH Keywords: lattice parallelotopes
zbMATH Keywords: combinatorial proof
reviewed by: Štefan Porubský
MaRDI profile type: Publication
cites work: New results for covering systems of residue sets
cites work: Roots of unity and covering sets
description: scientific article; zbMATH DE number 3983253