The toric h-vector of a cubical complex in terms of noncrossing partition statistics
arXiv:1302.5020
Abstract
This paper introduces a new and simple statistic on noncrossing partitions that expresses each coordinate of the toric -vector of a cubical complex, written in the basis of the Adin -vector entries, as the total weight of all noncrossing partitions. The same model may also be used to obtain a very simple combinatorial interpretation of the contribution of a cubical shelling component to the toric -vector. In this model, a strengthening of the symmetry expressed by the Dehn-Sommerville equations may be derived from the self-duality of the noncrossing partition lattice, exhibited by the involution of Simion and Ullman.