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On the Mobius function of a lower Eulerian Cohen-Macaulay Christos A. Athanasiadis

Summary: On the M¨obius function of a lower Eulerian Cohen-Macaulay
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
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 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.
Keywords: Eulerian poset, Cohen-Macaulay poset, M¨obius function, cubical h-vector, toric
h-vector, 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


Source: Athanasiadis, Christos - Department of Mathematics, University of Athens


Collections: Mathematics