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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2107.12459 |
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| _version_ | 1866908963303325696 |
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| 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 |