On m-covers and m-systems
| dc.creator | Sun, Zhi-Wei | |
| dc.date | 2004-03-16 | |
| dc.date | 2004-12-26 | |
| dc.date.accessioned | 2026-07-07T05:06:28Z | |
| dc.date.available | 2026-07-07T05:06:28Z | |
| dc.description | Let A={a_s(mod n_s)}_{s=0}^k be a system of residue classes. With the help of cyclotomic fields we obtain a theorem which unifies several previously known results concerning system A. In particular, we show that if every integer lies in more than m=[sum_{s=1}^k 1/n_s] members of A, then for any a=0,1,2,... there are at least binom{m}{[a/n_0]} subsets I of {1,...,k} with sum_{s in I}1/n_s=a/n_0. We also characterize when any integer lies in at most m members of A, where m is a fixed positive integer. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0403271 | |
| dc.identifier | http://arxiv.org/abs/math/0403271 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70481 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11B25; 05A05; 11A07; 11B75; 11D68 | |
| dc.title | On m-covers and m-systems | |
| dc.type | text |