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On the longest length of consecutive integers

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Abstract

Choose m numbers from the set {1, 2, …, n} at random without replacement. In this paper we first establish the limiting distribution of the longest length of consecutive integers and then apply the result to test randomness of selecting numbers without replacement.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, P. R. China

    Min Zhi Zhao

  2. Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, P. R. China

    Qi-Man Shao

Authors
  1. Min Zhi Zhao
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  2. Qi-Man Shao
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Corresponding author

Correspondence to Min Zhi Zhao.

Additional information

Dedicated to Professor Hua Loo-keng on his 100th birth anniversary

The first author is supported by National Natural Science Foundation of China (Grant Nos. 10601047, 11001070) and Zhejiang Provincial Natural Science Foundation of China (Grant No. J20091364); the second author is partially supported by Hong Kong RGC CERG (Grant Nos. 602608 and 603710)

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Zhao, M.Z., Shao, QM. On the longest length of consecutive integers. Acta. Math. Sin.-English Ser. 27, 329–338 (2011). https://doi.org/10.1007/s10114-011-0496-7

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  • DOI: https://doi.org/10.1007/s10114-011-0496-7

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