| Title:
|
Old and new necessary and sufficient conditions on $(a_i, m_i)$ in order that $n\equiv a_i (\operatorname {mod} m_i)$ be a covering system (English) |
| Author:
|
Porubský, Štefan |
| Author:
|
Schönheim, Jochanan |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
53 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
341-349 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11B25 |
| idZBL:
|
Zbl 1071.11012 |
| idMR:
|
MR2025467 |
| . |
| Date available:
|
2009-09-25T14:15:35Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/132814 |
| . |
| Reference:
|
[1] BEEBEE J.: Bernoulli covers and exact covering systems.Amer. Math. Monthly 99 (1992), 946-948. MR 1190561 |
| Reference:
|
[2] ERDÖS P.-GRAHAM R. L.: Old and New Problems in Combinatorial Number Theory.Monographic No. 28 de L'Enseigment Mathematique, Universite Geneneve, 1980. MR 0592420 |
| Reference:
|
[3] FRAENKEL A. S.: A characterization of exactly covering congruences.Discrete Math. 4 (1973), 359-366. Zbl 0257.10003, MR 0316359 |
| Reference:
|
[4] PORUBSKÝ Š.: Covering systems and generating functions.Acta Arith. 26 (1975), 223-231. Zbl 0268.10044, MR 0379423 |
| Reference:
|
[5] PORUBSKÝ Š.: On m-times covering systems.Acta Arith. 29 (1976), 159-169. Zbl 0282.10033, MR 0399033 |
| Reference:
|
[6] PORUBSKÝ Š.: Identities involving covering systems I.Math. Slovaca 44 (1994), 153-162. Zbl 0809.11012, MR 1282532 |
| Reference:
|
[7] PORUBSKÝ Š.-SCHÖNHEIM J.: Covering systems of Paul Erdös: past, present and future.In: Proceeding of the International Conference Paul Erdös and his Mathematics Budapest 1999 (G. Halász, L. Lovász, M. Simonovits, V .T. Sós, eds.), Bolyai Soc. Math. Stud. 11, Springer Verlag/János Bolyai Math. Society, Berlin-Heidelberg-New York/Budapest, 2002, pp. 581-627. MR 1954716 |
| Reference:
|
[8] PORUBSKÝ Š.-SCHÖNHEIM J.: New necessary and sufficient conditions on $(a_i,m_i)$ in order that $x = a_i$ (mod m) be a covering system.Discrete Math. (To appear). |
| Reference:
|
[9] SCHÖNHEIM J.: Covering congruences related to modular arithmetic and error correcting codes.Ars Combin. 16-B (1983), 21-25. Zbl 0535.10049, MR 0737106 |
| Reference:
|
[10] SUN Z.-W.: Several results and systems of residue classes.Math. China 18 (1989), 251-252. |
| Reference:
|
[11] ZNÁM Š.: A simple characterization of disjoint covering systems.Discrete Math. 12 (1975), 89-91. Zbl 0306.10001, MR 0376597 |
| . |
