Corpus ID: 236447908

The Variance and the Asymptotic Distribution of the Length of Longest $k$-alternating Subsequences

  title={The Variance and the Asymptotic Distribution of the Length of Longest \$k\$-alternating Subsequences},
  author={Altar cCicceksiz and Yunus Emre Demirci and Icslak},
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. 


On the Longest $k$-Alternating Subsequence
We show that the longest $k$-alternating substring of a random permutation has length asymptotic to $2(n-k)/3$.
Average length of the longest k-alternating subsequence
  • W. Cai
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 2015
It is shown that the k = 1 case is a well-known result of Richard Stanley and the conjecture on the average maximal length of k-alternating subsequence of permutations is true. Expand
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Enumerative Combinatorics Problem Session
  • 2014