# Princeton Discrete Math Seminar

## Title:

Geometry and poset probabilities

## Speaker:

- Jeff Kahn
- Rutgers University

## Place:

- Fine Hall 214
- Princeton University

## Time:

- 3:00 p.m.
- Thursday, April 17, 1997

Abstract:
We consider uniform distribution on the set of linear
extensions of a finite poset P. (A linear extension of P is a
linear ordering of the elements of P extending the order in P.)

Probabilities associated with such distributions are the subject
of several fascinating conjectures, some originating in questions
about sorting. Curiously, progress on these questions has usually
involved application of various tools from other parts of
mathematics, especially geometry.

We will survey some of these developments, and mention one new
result (joint with Yang Yu and answering a 1986 question of
Peter Fishburn), a special case of which says:

If x,y,z are elements of P for which Pr(x < y) > 1/2
and Pr(y < z) > 1/2, then Pr(x < z) > 1/4.

(Note nothing similar is true if we replace 1/2 by .499.)

Next week: TBA

Document last modified on April 11, 19997