What can be said about pure O-sequences?
Let \(f(\Delta)=(f_ 0,f_ 1,...,f_{d-1})\) be the f-vector of a Cohen- Macaulay complex \(\Delta\). Björner proved that (*) \(f_ i\leq f_{(d- 2)-i}\) for any \(0\leq i<[d/2]\) and \((**)\quad f_ 0\leq f_ 1\leq...\leq f_{[(d-1)/2]}.\) Recently, Stanley generalized Björner's inequalities (*) and (**) for pure simplicial complexes. In this paper we consider O- sequence analogue of the inequalities (*) and (**). Let \((h_ 0,h_ 1,...,h_ s),\quad h_ s\neq 0,\) is a pure O-sequence. We shall prove that \(h_ i\leq h_{s-i}\) for any \(0\leq i\leq [s/2]\) and \(h_ 0\leq h_ 1\leq...\leq h_{[(s+1)/2]}.\)
scientific article; zbMATH DE number 4091512