2 problems

Let $[n]=\{1,\ldots,n\}$ and let $\Delta\subseteq2^{[n]}$ be a strongly acyclic simplicial complex. Define the Winder desirability relation $\leq_W$ on $2^{[n]}$ by $A\leq_W B$ if…

Let $[n]=\{1,\ldots,n\}$ and let $\Delta\subseteq 2^{[n]}$ be a simplicial complex. Define the Winder desirability relation $\leq_W$ on $2^{[n]}$ by $A\leq_W B$ if and only if, for…