A characterization of covering equivalence
Number Theory
2007-10-22 v2 Combinatorics
Abstract
Let A={a_s(mod n_s)}_{s=1}^k and B={b_t(mod m_t)}_{t=1}^l be two systems of residue classes. If |{1\le s\le k: x=a_s (mod n_s)}| and |{1\le t\le l: x=b_t (mod m_t)}| are equal for all integers x, then A and B are said to be covering equivalent. In this paper we characterize the covering equivalence in a simple and new way. Using the characterization we partially confirm a conjecture of R. L. Graham and K. O'Bryant.
Cite
@article{arxiv.math/0409521,
title = {A characterization of covering equivalence},
author = {Hao Pan and Zhi-Wei Sun},
journal= {arXiv preprint arXiv:math/0409521},
year = {2007}
}