On cogrowth function of algebras and its logarithmical gap

A. J. Kanel-Belov, I. A. Melnikov, I. V. Mitrofanov

Let $A\cong k⟨X⟩/I$ be an associative algebra. A finite word over alphabet $X$ is $I${\it-reducible} if its image in $A$ is a $k$-linear combination of length-lexi…