The number of tiered posets modulo six (Q1086236)

A poset on an n-set is said to be tiered with height h if every element belongs to a maximal chain with exactly h elements. The author proves that the number of such posets (summed over all \(h=1,...,n)\) is congruent to 1 and 3 (mod 6) for n odd and even, respectively. Thus a conjecture of \textit{G. Kreweras} [Discrete Math. 53, 147-149 (1985; Zbl 0558.05004)] is verified.