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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.16113 |
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Table of 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.