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Proceedings of the American Mathematical Society

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Growth rates for monotone subsequences

Authors: A. del Junco and J. Michael Steele
Journal: Proc. Amer. Math. Soc. 71 (1978), 179-182
MSC: Primary 10K05
MathSciNet review: 0491571
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Abstract: The growth rate of the largest monotone subsequence of a uniformly distributed sequence is obtained. For $ {a_n} = n\alpha \bmod\; 1$ with $ \alpha $ algebraic irrational the exponent of growth is found to be precisely the same as for a random sequence.

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Keywords: Monotone subsequence, uniform distribution, algebraic irrationals, discrepancy
Article copyright: © Copyright 1978 American Mathematical Society