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Graham, R. L.

Covering the positive integers by disjoint sets of the form \(\{[n\alpha+\beta]: n=1,2,\dots \}\). (English) Zbl 0279.10042

J. Comb. Theory, Ser. A 15, 354-358 (1973).
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Cited in 2 Reviews
Cited in 28 Documents

MSC:

11B99 Sequences and sets
11A07 Congruences; primitive roots; residue systems
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\textit{R. L. Graham}, J. Comb. Theory, Ser. A 15, 354--358 (1973; Zbl 0279.10042)
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References:

[1] Bang, Th, On the sequence [nα], n = 1, 2,…, Math. scand., 5, 69-76, (1957) · Zbl 0084.04401
[2] Erdös, P, On integers of the form 2^{n} + p and some related problems, Summa brasil math., 2, 119, (1950)
[3] Erdös, P, On a problem concerning congruence systems, Mat. lapok, 3, 122-128, (1952)
[4] Fraenkel, A.S, The bracket function and complementary sets of integers, Canad. J. math., 21, 6-27, (1969) · Zbl 0172.32501
[5] Fraenkel, A.S, Complementing and exactly covering sequences, J. combinatorial theory, ser. A, 14, 8-20, (1973) · Zbl 0257.05023
[6] Graham, R.L, On a theorem of uspensky, Amer. math. monthly, 70, 407-409, (1963) · Zbl 0113.27101
[7] Niven, Ivan, Diophantine approximations, (1963), Interscience New York · Zbl 0115.04402
[8] Skolem, Th, Über einige eigenshaften der zahlenmengen [αn + β] bei irrationalem α mit einleitenden bermerkungen über einige kombinatorische probleme, Norske vid. selsk. forh. (Trondheim), 30, 118-125, (1957)
[9] Skolem, Th, On certain distributions of integers in pairs with given differences, Math. scand., 5, 57-68, (1957) · Zbl 0084.04304
[10] Stein, S.K, Unions of arithmetic sequences, Math. ann., 134, 289-294, (1958) · Zbl 0084.04302
[11] Uspensky, J.V, On a problem arising out of the theory of a certain game, Amer. math. monthly, 34, 516-526, (1927) · JFM 53.0167.05
[12] Znám, Ŝ, On exactly covering systems of arithmetic sequences, Math. ann., 180, 227-232, (1969) · Zbl 0169.37405
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.