A note on letters of Yangian invariants

Motivated by reformulating Yangian invariants in planar ${\cal N}=4$ SYM directly as $d\log$ forms on momentum-twistor space, we propose a purely algebraic problem of determining the arguments $d\log$'s, which call "letters", for any invariant. These are functions momentum twistors $Z$'s, given positive coordinates $\alpha$'s parametrizations matrix $C(\alpha)$, evaluated support polynomial equations $C(\alpha) \cdot Z=0$. We provide evidence that letters related to cluster algebra Grassmannian $G(4,n)$, is relevant symbol alphabet $n$-point scattering amplitudes. For $n=6,7$, collection all contains A}$ $G(4,n)$. determine invariant associated with "four-mass" box, $n=8$ reproduce $18$ multiplicative-independent, discovered recently two-loop