 
Summary: On the M¨obius function of a lower Eulerian CohenMacaulay
poset
Christos A. Athanasiadis
Department of Mathematics
University of Athens
Athens 15784, Hellas (Greece)
Email: caath@math.uoa.gr
May 16, 2011; revised, July 4, 2011
Abstract
A certain inequality is shown to hold for the values of the M¨obius function of the poset
obtained by attaching a maximum element to a lower Eulerian CohenMacaulay poset. In
two important special cases, this inequality provides partial results supporting Stanley's
nonnegativity conjecture for the toric hvector of a lower Eulerian CohenMacaulay meet
semilattice and Adin's nonnegativity conjecture for the cubical hvector of a CohenMacaulay
cubical complex.
Keywords: Eulerian poset, CohenMacaulay poset, M¨obius function, cubical hvector, toric
hvector, Buchsbaum complex.
1 Introduction
Let P be a finite poset which has a minimum element ^0 (for background and any undefined
terminology on partially ordered sets we refer the reader to [12, Chapter 3] and Section 2). Such
