2 problems

Let $p$ be a prime, and let $g_{(3,2,2,1,1)}(p)$ denote the quantity counting the relevant subring matrices associated with the composition $(3,2,2,1,1)$. Polynomial formula conjec…

Let $f_n(k)$ denote the number of subrings of ${\mathbb Z}^n$ having additive index $k$. For a real number $B>0$, let $N_n(B)$ denote the number of subrings of ${\mathbb Z}^n$ havi…