Codimension sequence, grade, and generating degree: an operadic approach

Abstract: We study several classes of operadic ideals of the unital associative algebra operad $\uas$. As an application, we classify quotient operads of $\uas$ of GK-dimension $\leq 6$. This corresponds to a classification of all T-ideals of codimension growth $n^g$ with $g\leq 5$ (or equivalently, varieties of grade $g$ with $g\leq 5$).