Algebraic Combinatorics Seminar - David Wagner

Thursday, March 18, 2021 1:00 pm - 1:00 pm EDT (GMT -04:00)

Title: The Poset Conjecture: results, counterexamples, and open problems

Speaker: David Wagner
Affiliation: University of Waterloo
Zoom: Contact Karen Yeats


In 1978, Neggers conjectured that a certain transform of the order polynomial of a partially ordered set (poset) has only real roots.

In the late 1980s, Stanley gave this to me as a thesis project, generalized to labelled posets.  For my thesis I proved the conclusion for series-parallel labelled posets and a bit more.  Br\"and\'en, and later Stembridge, found counterexamples to the conjecture in general.

But the conjecture remains open for some notable subclasses of the class of all posets.  Ferrers posets -- unknown -- clearly important.

Posets for which the Hasse (covering) graph is a tree might be possible.  The case in which the Hasse graph is a path is still open, but seems almost within reach given some new ideas.