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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.18281 |
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Table of Contents:
- Kaneko and Tsumura proved a relation of multiple $\tilde{T}$-values involving Entringer numbers counting the total number of down-up permutations starting with a fixed value. In the present paper, we generalize this relation and provide some relations involving Entringer numbers and the total number of Dumont permutations of the first kind starting with a fixed value. For this purpose, we also provide explicit formulas for the total numbers of those permutations.