Library

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

We obtain an explicit formula for the variance of the number of $k$-peaks in a uniformly random permutation. This is then used to obtain an asymptotic formula for the variance of the length of longest $k$-alternating subsequence in random permutations. Also a central limit is proved for the latter statistic.

Bayesian Methods and Mixture ModelsAdvanced Combinatorial MathematicsAlgorithms and Data Compression
Source

Paper

Similar papers

Mean and variance of the longest alternating subsequence in a random separable permutationRoss G. Pinsky2023 · arXiv (Cornell University) In Library
A Central Limit Theorem for Repeating PatternsAaron Abrams, Eric Babson, H. G. Landau et al.2026 · The Electronic Journal of Combinatorics In Library
Large deviations for the longest alternating and the longest increasing subsequence in a random permutation avoiding a pattern of length threeRoss G. Pinsky2023 · arXiv (Cornell University) In Library
Asymptotic expansions relating to the distribution of the length of longest increasing subsequencesFolkmar Bornemann2023 · arXiv (Cornell University) In Library
Variance of the number of cycles of random <i>A</i> -permutationA. L. Yakymiv2022 · Discrete Mathematics and Applications In Library
A Stirling-type formula for the distribution of the length of longest increasing subsequencesFolkmar Bornemann2022 · arXiv (Cornell University) In Library
Longest subsequence for certain repeated up/down patterns in random permutations avoiding a pattern of length threeRoss G. Pinsky2024 · arXiv (Cornell University) In Library
The Ulam-Hammersley problem for multiset permutationsLucas Gerin2023 · arXiv (Cornell University) In Library
On weak twins and up-and-down subpermutationsAndrzej Dudek, Jarosław Grytczuk, Andrzej Ruciński2022 In Library
On the Longest Common Subsequence of Conjugation Invariant Random PermutationsMohamed Slim Kammoun2020 · The Electronic Journal of Combinatorics In Library
© 2026 NYSGPT2525 LLC