Tight universality of $m$-gonal forms with minimal criterion sets

For integers $m\geq3$ and $n\geq1$, an $m$-gonal form is called tight $\mathcal{T}(n)$-universal if it represents exactly the positive integers $\mathcal{T}(n)=\{ n, n+1, n+2, \ldots \}$. In this paper, we study the minimal criterion set $\mathrm{CS}(m,n)$ for tight $\mathcal{T}(n)$-universality. Ou