Browsing by Subject "Longest increasing subsequences"

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    Longest increasing subsequences in involutions avoiding patterns of length three
    (TÜBİTAK, 2019-07) Mansour, T.; Yıldırım, Gökhan
    We study the longest increasing subsequences in random involutions that avoid the patterns of length three under the uniform probability distribution. We determine the exact and asymptotic formulas for the average length of the longest increasing subsequences for such permutation classes.
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    Variations on Hammersley’s interacting particle process
    (Shahin Digital Publisher, 2021-06) Atalık, Arda; Melihcan Erol, H. S.; Yıldırım, Gökhan; Yılmaz, Mustafa
    The longest increasing subsequence problem for permutations has been studied extensively in the last fifty years. The interpretation of the longest increasing subsequence as the longest 21-avoiding subsequence in the context of permutation patterns leads to many interesting research directions. We introduce and study the statistical properties of Hammersley type interacting particle processes related to these generalizations and explore the finer structures of their distributions. We also propose three different interacting particle systems in the plane analogous to the Hammersley process in one dimension and obtain estimates for the asymptotic orders of the mean and variance of the number of particles in the systems.