151. a. [2+] Let P be a p-element poset, and let S ⊆ [p − 1] such that βJ(P)(S) 0. Show that if T ⊆ S, then βJ (P)(T) 0.
b. [5–] Find a “nice” characterization of the collections Δ of subsets of [p − 1] for which there exists a p-element poset P satisfying
c. [2+] Show that (a) continues to hold if we replace J(P) with any finite supersolvable lattice L of rank p.
152. a. [2+] Let P be a finite naturally labeled poset. Construct explicitly ...