REU Students
#
REU Students

##
Summer 2000

Debbie Grier,
currently an undergrad at Cornell,
will be a graduate
student in mathematics at
Columbia University
in Fall 2002.

Geir Helleloid,
currently an undergrad at Wisconsin--Madison,
will be a graduate
student in mathematics at
Stanford University
in Fall 2002.

Michael Levin,
a 2001 Harvard graduate,
is studying Theoretical Physics at MIT.

**
Michael's research won Honorable Mention for the
2001
Morgan Prize.
**
This is a prize given for outstanding
undergraduate research
in mathematics.

Adnan Rubai,
a 2001 graduate of Binghamton University,
is a graduate student in mathematics
at Binghamton University.

**
References:
**

A probabilistic approach to the descent statistic,
by R. Ehrenborg, M. Levin and M. Readdy,
*
Journal of Combinatorial Theory,
Series A,
*
**
98
**
(2002), 150-162.

Quadratic inequalities for the descent set of
permutations are developed using a probabilistic
reformulation of the descent statistic.

##
Summer 1997

Dan Johnston is currently an undergrad at Washington University in St. Louis.

Mohan Rajagopalan,
an Oberlin undergrad,
is
currently a graduate student in Logic at Cornell.

Harold Fox entered the MIT Artificial Intelligence Lab in Fall 2001.

**
References:
**

Cutting polytopes and
flag f-vectors,
by
R. Ehrenborg,
D. Johnston,
R. Rajagopalan
and M. Readdy,
*
Discrete and Computational Geometry,
*
**
23
**
(2000), 261-271.
We show how the flag f-vector
changes
when cutting off any
face
of a polytope.
The result is expressed in terms of
explicit linear operators on **cd**-polynomials.
The operation of
contracting any face of the polytope
is also considered.

Inequalities for
**cd**-indices of joins and products of polytopes,
by
R. Ehrenborg
and H. Fox,
to appear
in *
Combinatorica.
*
Explicit expressions for the
**cd**-index
of the free join of two polytopes and the Cartesian
product
in terms of the **cd**-basis
are determined,
as well as an inequality relating these two
operations on polytopes. This inequality gives
evidence for Stanley's conjecture on Gorenstein* lattices.