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.
A Probabilistic Approach to the Asymptotics of the Length of the Longest Alternating Subsequence
The methodology is robust enough to tackle similar problems for finite alphabet random words or even Markovian sequences, and a sketch of how some cases of pattern restricted permutations can also be tackled with probabilistic methods is presented.
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Let asn denote the length of a longest alternating subsequence in a uniformly random permutation of order n. Stanley studied the distribution of asn using algebraic methods, and showed in particular
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Enumerative Combinatorics Problem Session
  • 2014