The Variance and the Asymptotic Distribution of the Length of Longest $k$-alternating Subsequences
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908963303325696 |
|---|---|
| author | Çiçeksiz, Recep Altar Demirci, Yunus Emre Işlak, Ümit |
| author_facet | Çiçeksiz, Recep Altar Demirci, Yunus Emre Işlak, Ümit |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_12459 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Variance and the Asymptotic Distribution of the Length of Longest $k$-alternating Subsequences Çiçeksiz, Recep Altar Demirci, Yunus Emre Işlak, Ümit Probability Combinatorics 05A05 (Primary), 60F05 (Secondary) 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. |
| title | The Variance and the Asymptotic Distribution of the Length of Longest $k$-alternating Subsequences |
| topic | Probability Combinatorics 05A05 (Primary), 60F05 (Secondary) |
| url | https://arxiv.org/abs/2107.12459 |