5 problems

Let $k$ be a positive integer, and for each $i=1,\dots,k$ let $n_i$ be a positive integer. Write $[n_i]$ for the corresponding finite chain, let $[n_1] \times \dots \times [n_k]$ b…

Let $p$ be prime, let $G=(C_p)^n$, and let $\binom{n}{k}_p$ denote the Gaussian binomial coefficient, counting the subgroups of $C_p^n$ isomorphic to $C_p^k$. Let $\mathfrak{c}(G)$…

Let $p$ and $q$ be distinct primes, let $n\geqslant m\geqslant2$, and let $\mathfrak{c}(C_{p^nq^m})$ denote the complexity. Let $\operatorname{SR}(n,m)$ and…

Let $p$ and $q$ be distinct primes and let $n\geqslant m\geqslant2$. Write $\mathfrak{c}(C_{p^nq^m})$ for the complexity of $C_{p^nq^m}$. A simple rainbow and a double rainbow are…

Let $p$ and $q$ be distinct primes, and let $G=C_{p^nq^m}$. A simple rainbow and a double rainbow are the rainbow constructions defined in the paper; write $\mathfrak{c}(G)$ for th…