Average length of the longest k-alternating subsequence

@article{Cai2015AverageLO,
  title={Average length of the longest k-alternating subsequence},
  author={W. Cai},
  journal={J. Comb. Theory, Ser. A},
  year={2015},
  volume={134},
  pages={51-57}
}
  • W. Cai
  • Published 5 February 2015
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
We prove a conjecture of Drew Armstrong on the average maximal length of k-alternating subsequence of permutations. The k = 1 case is a well-known result of Richard Stanley. 
The Variance and the Asymptotic Distribution of the Length of Longest $k$-alternating Subsequences
We obtain an explicit formula for the variance of the length of longest k-alternating subsequence in a uniformly random permutation. Also a central limit is proved for the same statistic.

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