论文标题
交替多个$ t $ - 价值：加权总和，双重性和维度猜想
Alternating Multiple $T$-Values: Weighted Sums, Duality, and Dimension Conjecture
论文作者
论文摘要
在本文中，我们定义了一些交替的多个$ t $价值（AMTV）的加权总和，并通过使用我们以前的论文中开发的工具来研究它们的几种双重性公式。然后，我们介绍了复杂的$ t $价值和kaneko-tsumura $ψ$功能的交替版本，事实证明，它们与AMTV密切相关。在论文的结尾，我们研究了由任何固定重量$ w $的AMTV产生的$ \ q $ - 向量空间，并提供了一些猜想的证据，表明其尺寸$ \ {d_w \} _ {w \ ge 1}
In this paper, we define some weighted sums of the alternating multiple $T$-values (AMTVs), and study several duality formulas for them by using the tools developed in our previous papers. Then we introduce the alternating version of the convoluted $T$-values and Kaneko-Tsumura $ψ$-function, which are proved to be closely related to the AMTVs. At the end of the paper, we study the $\Q$-vector space generated by the AMTVs of any fixed weight $w$ and provide some evidence for the conjecture that their dimensions $\{d_w\}_{w\ge 1}$ form the tribonacci sequence 1, 2, 4, 7, 13, ....
