On the Möbius function of a lower Eulerian Cohen–Macaulay poset

摘要

A certain inequality is shown to hold for the values of the Möbius function of the poset obtained by attaching a maximum element to a lower Eulerian Cohen–Macaulay poset. In two important special cases, this inequality provides partial results supporting Stanley’s nonnegativity conjecture for the toric h-vector of a lower Eulerian Cohen–Macaulay meet-semilattice and Adin’s nonnegativity conjecture for the cubical h-vector of a Cohen–Macaulay cubical complex.