IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

## 28th Cumberland Conference on Combinatorics, Graph Theory & Computing

Gábor Hetyei
University of North Carolina, Charlotte
http://math2.uncc.edu/~ghetyei/
Abstract

## Cubical $h$-vectors, noncrossing partitions, and Catalan numbers

• Authors: Sarah Birdsong & Gábor Hetyei
• May 16, 2015
• 3:30 p.m.
• Gambrell 152

After a brief introduction to $h$-vectors of cubical complexes, we express each coordinate of Stanley's toric $h$-vector, written in the basis of the Adin $h$-vector entries, as the total weight of all noncrossing partitions in a weighted enumeration model. In our model, the symmetry expressed by the Dehn-Sommerville equations is a consequence of the self-duality of the non-crossing partition lattice, exhibited by the involution of Simion and Ullman. By collecting the appropriate terms we also obtain a new, very simple combinatorial interpretation of the contribution of a shelling component to the toric h-vector of a cubical complex.

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