The variance and the asymptotic distribution of the length of longest k-alternating subsequences

被引：0

作者：

Ciceksiz, Recep Altar ^{[1
]}

Demirci, Yunus Emre ^{[2
]}

Islak, Umit ^{[3
]}

机构：

[1] Umea Univ, Dept Math, Umea, Sweden

[2] Queens Univ, Dept Math & Stat, Kingston, ON, Canada

[3] Bogazici Univ, Dept Math, Istanbul, Turkiye

来源：

DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE | 2023年 / 25卷 / 01期

关键词：

Alternating subsequences; k-alternating subsequences; Peak; central limit theorem; SUMS;

D O I：

10.46298/DMTCS.10296

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

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.

引用

页数：9

共 50 条

[31] Constrained longest common subsequences with run-length-encoded strings
Liu, Jia-Jie (jjliu@cc.shu.edu.tw), 1600, Oxford University Press (58):
[32] A probabilistic approach to the asymptotics of the length of the longest alternating subsequence
Houdre, Christian
Restrepo, Ricardo
ELECTRONIC JOURNAL OF COMBINATORICS, 2010, 17 (01):
[33] Average length of the longest increasing subsequences in random involutions avoiding 231 and a layered pattern
Mansour, Toufik
Song, Chunwei
DISCRETE MATHEMATICS LETTERS, 2020, 4 : 56 - 59
[34] Optimal Online and Offline Algorithms for Finding Longest and Shortest Subsequences with Length and Sum. Constraints
Kim, Sung Kwon
IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS, 2010, E93D (02) : 250 - 256
[35] Large deviations-based upper bounds on the expected relative length of longest common subsequences
Hauser, Raphael
Martinez, Servet
Matzinger, Heinrich
ADVANCES IN APPLIED PROBABILITY, 2006, 38 (03) : 827 - 852
[36] Longest Common Subsequence in k Length Substrings
Benson, Gary
Levy, Avivit
Shalom, B. Riva
SIMILARITY SEARCH AND APPLICATIONS (SISAP), 2013, 8199 : 257 - 265
[37] Large deviations for the longest alternating and the longest increasing subsequence in a random permutation avoiding a pattern of length three
Pinsky, Ross G.
ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2024, 29
[38] On the length of longest alternating paths for multicoloured point sets in convex position
Merino, C.
Salazar, G.
Urrutia, J.
DISCRETE MATHEMATICS, 2006, 306 (15) : 1791 - 1797
[39] On zero-sum subsequences of length k exp(G)
Gao, Weidong
Han, Dongchun
Peng, Jiangtao
Sun, Fang
JOURNAL OF COMBINATORIAL THEORY SERIES A, 2014, 125 : 240 - 253
[40] A Note on the Expected Length of the Longest Common Subsequences of two i.i.d. Random Permutations
Houdre, Christian
Xu, Chen
ELECTRONIC JOURNAL OF COMBINATORICS, 2018, 25 (02):

← 1 2 3 4 5 →