Papers in progress

(See also my published papers.)

Russ Woodroofe, Chordal and sequentially Cohen-Macaulay clutters.
pdf
Abstract. We extend the definition of chordal from graphs to clutters. The resulting family generalizes both chordal graphs and matroids, and obeys many of the same algebraic and geometric properties. Specifically, the independence complex of a chordal clutter is shellable, hence sequentially Cohen-Macaulay; and the circuit ideal of a certain complement to such a clutter has a linear resolution. Minimal non-chordal clutters are also closely related to obstructions to shellability, and we give some general families of such obstructions, together with a classification by computation of all obstructions to shellability on 6 vertices.
The shelling of the independence complex is constructed by extending the definitions of shedding face and k-decomposability to non-pure complexes. The resulting tool to construct shellings may be of independent interest.