A sharp result on m-covers
| dc.creator | Pan, Hao | |
| dc.creator | Sun, Zhi-Wei | |
| dc.date | 2005-04-20 | |
| dc.date | 2006-09-09 | |
| dc.date.accessioned | 2026-07-07T06:39:49Z | |
| dc.date.available | 2026-07-07T06:39:49Z | |
| dc.description | Let A={a_s+n_sZ}_{s=1}^k be a finite system of arithmetic sequences which forms an m-cover of Z (i.e., every integer belongs at least to m members of A). In this paper we show the following sharp result: For any positive integers m_1,...,m_k and theta in [0,1), if there is a subset I of {1,...,k} such that the fractional part of sum_{s in I}m_s/n_s is theta, then there are at least 2^m such subsets of {1,...,k}. This extends an earlier result of M. Z. Zhang and an extension by Z. W. Sun. Also, we generalize the above result to m-covers of the integral ring of any algebraic number field with a power integral basis. | |
| dc.description | 7 pages, to appear in Proc. Amer. Math. Soc | |
| dc.identifier | https://arxiv.org/abs/math/0504413 | |
| dc.identifier | http://arxiv.org/abs/math/0504413 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101220 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11B25; 11B75; 11D68; 11R04 | |
| dc.title | A sharp result on m-covers | |
| dc.type | text |