Some papers by John Shareshian

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 2-connected 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 2-connected 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 2-connected graphs on n vertices are examined. The results allow one to determine the homotopy type of the complex of not 2-connected, 3-regular 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. 703-707. 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 t-colorable 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>n-4. 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 q-Eulerian polynomials
(with Michelle Wachs, submitted).

Last modified: January 15, 2009