Large Discrepancy In Homogenous Quasi-Arithmetic Progressions |
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Authors: | Robert Hochberg |
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Affiliation: | (1) Department of Computer Science, East Carolina University, Greenville, NC 27858, USA |
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Abstract: | We prove that the class of homogeneous quasi-arithmetic progressions has unbounded discrepancy. That is, we show that given any 2-coloring of the natural numbers and any positive integer D, one can find a real number α≥1 and a set of natural numbers of the form {0, [α], [2α], [3α], . . . , [kα]} so that one color appears at least D times more than the other color. This was already proved by Beck in 1983, but the proof given here is somewhat simpler and gives a better bound on the discrepancy. |
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Keywords: | 11B25 11K38 05C15 |
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