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arXiv · 2404.18281

Relations of multiple $\tilde{T}$-values involving the total numbers of certain permutations

Ryota Umezawa
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Abstract

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.

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Ryota Umezawa. 2024-04-28. Relations of multiple $\tilde{T}$-values involving the total numbers of certain permutations. https://arxiv.org/abs/2404.18281

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