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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.01687 |
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| _version_ | 1866910570672816128 |
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| author | Asakly, Walaa Kezil, Noor |
| author_facet | Asakly, Walaa Kezil, Noor |
| contents | The aim of this paper is to derive explicit formulas for two distinct values. The first is the total number of symmetric peaks in a set partition of $[n]$ with exactly $k$ blocks, and the second one is the total number of non-symmetric peaks in a set partition of $[n]$ with exactly $k$ blocks. We represent these results in two ways. First by using the theory of generating functions, and the second by using combinatorial tools. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01687 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Counting symmetric and non-symmetric peaks in a set partition Asakly, Walaa Kezil, Noor Combinatorics The aim of this paper is to derive explicit formulas for two distinct values. The first is the total number of symmetric peaks in a set partition of $[n]$ with exactly $k$ blocks, and the second one is the total number of non-symmetric peaks in a set partition of $[n]$ with exactly $k$ blocks. We represent these results in two ways. First by using the theory of generating functions, and the second by using combinatorial tools. |
| title | Counting symmetric and non-symmetric peaks in a set partition |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2401.01687 |