Prime covers and periodic patterns

Kurzfassung/Abstract

The work of I. Korec on irreducible (prime) disjoint covering systems of residue classes is continued. We exploit combinatorial methods to obtain two new existence theorems. First, one can prescribe the number s of occurrences of a certain modulus in a prime cover, provided s is small enough. Second, there are prime covers without supremum, provided the order is divisible by sufficiently many different primes.