Symbol alphabets from plabic graphs II: rational letters

A bstract Symbol alphabets of n -particle amplitudes in N = 4 super-Yang-Mills theory are known to contain certain cluster variables of G(4 , n ) as well as certain algebraic functions of cluster variables. The first paper arXiv:2007.00646 in this series focused on n = 8 algebraic letters. In this paper we show that it is possible to obtain all rational symbol letters (in fact all cluster variables) by solving matrix equations of the form C Z = 0 if one allows C to be an arbitrary cluster parameterization of the top cell of G + ( n− 4 , n ).