The University of Michigan Combinatorics Seminar


Abstract 

The title refers to two seemingly unrelated open combinatorial
conjectures from the late 1980's/early 1990's. The CharneyDavis
Conjecture asserts an inequality on face numbers of certain simplicial
spheres. The NeggersStanley Conjecture asserts that certain generating
functions (counting linear extensions of a poset by number of descents)
have only real zeroes. 