Counting up-up-or-down-down permutations
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915032923635712 |
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| author | Gessel, Ira M. |
| author_facet | Gessel, Ira M. |
| contents | Answering a question of Donald Knuth, we find the bivariate exponential generating function for "up-up-or-down-down'' permutations of odd length according to their last entry. An up-up-or-down-down permutation is a permutation $a_1a_2\cdots a_n$ satisfying $a_{2i-1}<a_{2i}$ if and only if $a_{2i}<a_{2i+1}$ for $1\le i <n/2$. Equivalently, an up-up-or-down-down permutation is one in which every peak and every valley is odd. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16113 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Counting up-up-or-down-down permutations Gessel, Ira M. Combinatorics Answering a question of Donald Knuth, we find the bivariate exponential generating function for "up-up-or-down-down'' permutations of odd length according to their last entry. An up-up-or-down-down permutation is a permutation $a_1a_2\cdots a_n$ satisfying $a_{2i-1}<a_{2i}$ if and only if $a_{2i}<a_{2i+1}$ for $1\le i <n/2$. Equivalently, an up-up-or-down-down permutation is one in which every peak and every valley is odd. |
| title | Counting up-up-or-down-down permutations |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2411.16113 |