Strongly signable and partitionable posets (Q1372625)

During the last twenty years there were several attempts to generalize the notion of \textsl{shellability} of simplicial complexes, motivated by the existence of non-shellable triangulated spheres. For example, the class of \textsl{partitionable complexes}, considered by L. J. Billera, J. S. Provan, R. P. Stanley and others [see \textit{G. M. Ziegler}, Lectures on polytopes (1995; Zbl 0823.52002)] includes all shellable complexes and possibly, all triangulated spheres. A poset is partitionable if its chain complex is. In searching for sufficient conditions for a poset to be partitionable, R. P. Stanley, A. Björner and M. Wachs introduced a class of \textsl{ \textit{CR}-posets}. In this article [which is a continuation of Discrete Comput. Geom. 15, 443-466 (1996; Zbl 0853.52010)] the author introduces the class of \textsl{strongly signable} posets, which are dual \textit{CR} and hence partitionable. He also proves that the barycentric subdivision of a partitionable complex is again partitionable.