English

On the reducibility of exact covering systems

Combinatorics 2015-06-03 v2

Abstract

There exist irreducible exact covering systems (ECS). These are ECS which are not a proper split of a coarser ECS. However, an ECS admiting a maximal modulus which is divisible by at most two distinct primes, primely splits a coarser ECS. As a consequence, if all moduli of an ECS AA, are divisible by at most two distinct primes, then AA is natural. That is, AA can be formed by iteratively splitting the trivial ECS.

Keywords

Cite

@article{arxiv.1402.3957,
  title  = {On the reducibility of exact covering systems},
  author = {Ofir Schnabel},
  journal= {arXiv preprint arXiv:1402.3957},
  year   = {2015}
}