2 problems

Let $X$ be a set, and let $\mathcal{T}(X)$ denote the full transformation semigroup on $X$. For the notation $N^{X}_{x_1,\ldots,x_t}$ and the functions $\xi$ and $\alpha$, use the…

Let ${\rm C}_{k;n}$ be a cyclic commutative semigroup with parameters $k$ and $n$, and let ${\hat{\sl l}}({\rm C}_{k;n})$ denote the threshold associated with idempotent-sum-free s…