Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.16113 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915032923635712 |
|---|---|
| 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 |