Alternating multiple T -values: weighted sums, duality, and dimension conjecture

In this paper, we define some weighted sums of the alternating multiple T -values (AMTVs) and study several duality formulas for them. 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≥ 1 form the tribonacci sequence 1, 2, 4, 7, 13, ....