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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
DOI: https://doi.org/10.1090/S0002-9939-1978-0491571-6
MathSciNet review: 0491571
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0491571-6
Keywords: Monotone subsequence, uniform distribution, algebraic irrationals, discrepancy
Article copyright: © Copyright 1978 American Mathematical Society