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Enumerative Combinatorics, Second Edition by Richard P. Stanley

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151.  a.  [2+] Let P be a p-element poset, and let S ⊆ [p − 1] such that βJ(P)(S) image 0. Show that if TS, then βJ (P)(T) image 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

image

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 ...

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