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Irregularities of two-colourings of the NxN square lattice. (English) Zbl 0501.10052

MSC:

11K38 Irregularities of distribution, discrepancy
05C55 Generalized Ramsey theory
11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension

Citations:

Zbl 0125.296
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References:

[1] J. Beck, Roth’s estimate of the discrepancy of integer sequences is nearly sharp,Combinatorica 1 (4) (1981), 319–325. · Zbl 0491.10046 · doi:10.1007/BF02579452
[2] J. Beck, Balanced two-colorings of finite sets in the square. I,Combinatorica 1 (4) (1981) 327–339. · Zbl 0491.10043 · doi:10.1007/BF02579453
[3] J. Beck andT. Fiala, ”Integer-making” theorems,Discrete Applied Math. 3 (1981) 1–8. · Zbl 0473.05046 · doi:10.1016/0166-218X(81)90022-6
[4] H. Chernoff, A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations,Ann. Math. Stat. 23 (1952) 493–509. · Zbl 0048.11804 · doi:10.1214/aoms/1177729330
[5] P. Erdos andJ. Spencer,Probabilistic Methods in Combinatorics, Akadémiai Kiadó, Budapest, 1974.
[6] G. Herman, Sums of distances between points on a sphere,to appear.
[7] K. F. Roth, Remark concerning integer sequences,Acta Arithmetica 9 (1964), 257–260. · Zbl 0125.29601
[8] W. M. Schmidt, Irregularities of distribution. II.Trans. Am. Math. Soc. 136 (1969), 347–360. · Zbl 0175.33102 · doi:10.1090/S0002-9947-1969-0234923-0
[9] W. M. Schmidt, Irregularities of distribution. IV.Inv. Math. 7 (1969), 55–82. · Zbl 0172.06402 · doi:10.1007/BF01418774
[10] W. M. Schmidt, Lectures on irregularities of distribution,Tata Inst. of Fund. Res. Lectures on Math. and Phys. 56 (1977). · Zbl 0434.10031
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