Preprints

(See also my published papers.)

Citation counts are taken from Google Scholar, which on occasion overcounts slightly.

  • Anton Dochtermann, Ritika Nair, Jay Schweig, Adam Van Tuyl, and Russ Woodroofe, Simplicial complexes with many facets are vertex decomposable, preprint.

    Let Δ be a pure simplicial complex on n vertices having dimension d and codimension c = nd − 1 in the simplex. Terai and Yoshida proved that if the number of facets of Δ is at least n choose c − 2c + 1, then Δ is Cohen-Macaulay. We improve this result by showing that these hypotheses imply the stronger condition that Δ is vertex decomposable. We give examples to show that this bound is optimal, and that the conclusion cannot be strengthened to the class of matroids or shifted complexes. We explore an application to Simon's Conjecture and discuss connections to other results from the literature.

  • Robert M. Guralnick, John Shareshian, and Russ Woodroofe, Invariable generation of finite simple groups and rational homology of coset posets, submitted.
    Attachments: GAP code, input, and output.

    We show that every finite simple group is generated invariably by a Sylow subgroup and a cyclic group. It follows that that the order complex of the coset poset of an arbitrary finite group has nontrivial reduced rational homology.