A conjecture about multiple $t$-values

TL;DR

This paper proposes a conjectural basis for the vector space generated by multiple t-values of a fixed weight, relating its dimension to Fibonacci numbers as predicted by Hoffman.

Contribution

It introduces a conjectural basis for the space of multiple t-values, supporting Hoffman's prediction about its dimension being Fibonacci numbers.

Findings

Conjectural basis for multiple t-values space proposed

Supports Hoffman's Fibonacci dimension prediction

Provides a new perspective on multiple t-values structure

Abstract

For positive integers $a_1,\ldots,a_r$ with $a_1 \ge 2$, the multiple $t$-value $t(a_1,\ldots,a_r)$ is defined by the series $\sum\limits_{n_1 > \ldots > n_r > 0 \atop n_i \text{ odd}} n_1^{-a_1} \cdots n_r^{-a_r}$. For an integer $k \ge 2$, the dimension of the $\mathbb Q$-vector space generated by all the multiple $t$-values of weight $k$ has been predicted by Hoffman to be the $k$-th Fibonacci number. In this short note we give a conjectural basis of this vector space.