|
New results for covering systems of residue sets
Author(s):
Marc A.
Berger;
Alexander
Felzenbaum;
Aviezri S.
Fraenkel
Journal:
Bull. Amer. Math. Soc.
14
(1986),
121-125.
MSC (1980):
Primary 11A07, 11B75, 11H31, 11B25, 20D15, 20D60, 51A15
MathSciNet review:
818066
Retrieve article in:
PDF
References |
Similar articles |
Additional information
References:
- 1.
- M. A. Berger, A. Felzenbaum and A. S. Fraenkel, A non-analytic proof of the Newman-Znám result for disjoint covering systems, Combinatorica (to appear).
- 2.
- M. A. Berger, A. Felzenbaum and A. S. Fraenkel, Lattice parallelepipeds and disjoint covering systems, Department of Mathematics, The Weizmann Institute of Science, May 1984. (Currently being revised.)
- 3.
- M. A. Berger, A. Felzenbaum and A. S. Fraenkel, The Herzog-Schönheim conjecture for finite nilpotent groups, Canad. Math. Bull. (to appear). MR 846712
- 4.
- M. A. Berger, A. Felzenbaum and A. S. Fraenkel, Disjoint covering systems of rational Beatty sequences, J. Combini. Theory A (to appear). MR 843471
- 5.
- M. A. Berger, A. Felzenbaum and A. S. Fraenkel, Necessary condition for the existence of an incongruent covering system with odd moduli, Acta Arith. (to appear). MR 893463
- 6.
- M. A. Berger, A. Felzenbaum and A. S. Fraenkel, Improvements to the Newman-Znám result for disjoint covering systems, Acta Arith. (to appear). MR 945272
- 7.
- M. A. Berger, A. Felzenbaum and A. S. Fraenkel, Improvements to two results concerning systems of residue sets, Ars Combin. (to appear). MR 824850
- 8.
- M. A. Berger, A. Felzenbaum and A. S. Fraenkel, Covers of product sets and the Korec-Znám result, Department of Mathematics, The Weizmann Institute of Science, November, 1984.
- 9.
- M. A. Berger, A. Felzenbaum and A. S. Fraenkel, Disjoint covering systems with precisely one multiple modulus, Department of Mathematics, The Weizmann Institute of Science, January, 1985.
- 10.
- M. A. Berger, A. Felzenbaum and A. S. Fraenkel, Remark on the multiplicity of a partition of a group into cosets, Fund. Math. (to appear). MR 922566
- 11.
- N. Burshtein, On natural exactly covering systems of congruences having moduli occurring at most M times, Discrete Math. 14 (1976), 205-214. MR 399035
- 12.
- R. F. Churchhouse, Covering sets and systems of congruences, Computers in Mathematical Research (R. F. Churchhouse and J.-C. Herz, eds.), North-Holland, Amsterdam, 1968, pp. 20-36. MR 240045
- 13.
- P. Erdős, On a problem concerning covering systems (Hungarian; English summary), Mat. Lapok. 3 (1952), 122-128. MR 70651
- 14.
- P. Erdős and R. L. Graham, Old and new problems and results in combinatorial number theory, Monographie No. 28 de L'Enseignement Mathématique, Université de Genève, 1980. MR 592420
- 15.
- A. S. Fraenkel, Complementing and exactly covering sequences, J. Combin. Theory 14 (1973), 8-20. MR 309770
- 16.
- R. K. Guy, Unsolved problems in number theory, Springer-Verlag, New York, N. Y., 1981. MR 656313
- 17.
- M. Herzog and J. Schönheim, Research problem no. 9, Canad. Math. Bull. 17 (1974), 150.
- 18.
- I. Korec, On a generalization of Mycielski's and Znám's conjectures about coset decomposition of Abelian groups, Fund. Math. 85 (1974), 41-48. MR 357557
- 19.
- M. Newman, Roots of unity and covering sets, Math. Ann. 191 (1971), 279-282. MR 286763
- 20.
- Š. Porubský, Generalization of some results for exactly covering systems, Mat. Casopis Sloven. Akad. Vied 22 (1972), 208-214. MR 308021
- 21.
- Š. Porubský, Results and problems on covering systems of residue classes, Mitteilungen aus dem Math. Sem. Giessen, Heft 150, Universität Giessen, 1981. MR 638657
- 22.
- S. K. Stein, Unions of arithmetic sequences, Math. Ann. 134 (1958), 289-294. MR 93493
- 23.
- Š. Znám, On exactly covering systems of arithmetic sequences, Math. Ann. 180 (1969), 227-232. MR 242760
- 24.
- Š. Znám, On exactly covering systems of arithmetic sequences, Number Theory, Colloq. Math. Societatis János Bolyai Vol. 2 (P. Turán, ed.), Debrecen, 1968, North-Holland, Amsterdam, 1970, pp. 221-225. MR 272705
- 25.
- Š. Znám, On properties of systems of arithmetic sequences, Acta Arith. 26 (1975), 279-283. MR 379424
- 26.
- Š. Znám, A survey of covering systems of congruences, Acta Mathematica Universitatis Comenianae 40-41 (1982), 59-78. MR 686961
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(1980):
11A07, 11B75, 11H31, 11B25, 20D15, 20D60, 51A15
Retrieve articles in all Journals with MSC
(1980):
11A07, 11B75, 11H31, 11B25, 20D15, 20D60, 51A15
Additional Information:
DOI:
10.1090/S0273-0979-1986-15414-5
PII:
S 0273-0979(1986)15414-5
|