
On the shellability of the order complex of the
subgroup lattice of a finite group
 This will appear in Transactions of the AMS. It
contains a proof that the order complex of the subgroup lattice of a finite
group G is shellable if and only if G is solvable.

Discrete Morse theory for the complex of
2connected graphs
 This will appear in Topology. Using the
discrete Morse theory of R. Forman, a basis is found for the unique nontrivial
homology group of the complex of 2connected graphs. This solves a problem
posed by V. Vassiliev.

Links in the complex of separable graphs
 This appeared in Journal of Combinatorial Theory, Series
A 88 (1999). Links in the complex of not 2connected graphs on n vertices
are examined. The results allow one to determine the homotopy type of the
complex of not 2connected, 3regular hypergraphs, knowledge of which is
of some use in the theory of Vassiliev invariants of ornaments.

On the probabalistic zeta function for finite
groups
 This appeared in Journal of Algebra 210 (1998), pp. 703707.
It contains a proof of a conjecture of Nigel Boston on the value of the
derivative of the probabalistic zeta function evaluated at s=1.

Combinatorial properties of subgroup lattices of finite groups
 My PhD thesis, which was written under the
direction of Richard Lyons at Rutgers University in New Brunswick, NJ,
completed in May 1996. Some nonmathematical pages at the beginning
appear twice for some strange reason.

Enumerating representation in wreath products
II: Explicit formulae
 (with Thomas M\"uller, submitted for publication) Using
earlier work of M\"uller, we produce an explicit formula for the
exponential generating function for Hom(G,R_n), where G is a finite
abelian or dihedral group and {R_n} (n=0 to infinity) is one of
several series of semidirect products, namely the series of Weyl groups
of type D and the series of wreath products {S_n[H]} and {A_n[H]} for
certain finite groups H.

Complexes of tcolorable graphs
 (with Svante Linusson, submitted for publication)
We examine the simplicial complex of all graphs on n vertices which
can be properly colored with t colors. We determine the homotopy
type of this complex when t=2 and when t>n4. In each case we obtain
a wedge of spheres, all of the same dimension. However, this
phenomenon does not occur when n=8 and t=4.

Eulerian quasisymmetric functions
 (with Michelle Wachs, submitted).

Poset homology of Rees products, and qEulerian polynomials
 (with Michelle Wachs, submitted).

Last modified: January 15, 2009