2 problems

Let $P$ be a poset, and consider the induced saturation function $\mathrm{sat}^{\star}([t]^n,P)$ whenever it is defined. Monotonicity conjecture. The function…

Let $P$ be a poset and fix $t\in\mathbb{Z}_{\geq 2}$. Write $\mathrm{sat}^{\star}([t]^n,P)$ for the induced saturation function of $P$ in the $t$-ary hypergrid. Linear-growth dicho…