## Counting chains in graded partially ordered sets

- March 5, 2002
- 3:30 p.m.
- LeConte 312

## Abstract

Part of the effort to generalize the Kruskal-Katona theorem to balanced simplicial complexes involves studying the number of partial chains hitting a fixed set of ranks in a graded partially ordered set. Together with Louis Billera we have found a method to find all linear inequalities holding for these numbers in an arbitrary graded poset. The method used allows for more specific results for specific classes of graded posets, such as planar posets. Together with Margaret Bayer we used the same basic idea to extract some information on the same invariants for graded Eulerian posets.