New Hoffman-type generators for alternating multiple zeta values

We introduce multiple $s$ values and prove that every alternating multiple zeta value is a $\mathbb{Q}$-linear combination of multiple $s$ values $s(k_1,\dots ,k_r)$ with $k_i\in \{1,2\}$. We also study when certain multiple $s$ values can be expressed as $\mathbb{Q}$-linear combinations of multiple zeta values.