Preprints
(See also my published papers and my research overview.)
Citation counts are taken from Google Scholar, which on occasion overcounts slightly.
- Robert M. Guralnick, John Shareshian, and Russ Woodroofe, Infinitely many finite simple groups of Lie type are not generated invariably by two elements of prime order, preprint.
We show that there are infinitely many k for which Sp2k(2) is not generated invariably by two elements of prime order.
- Stephan Foldes and Russ Woodroofe, Antichain cutsets in real-ranked lattices, preprint.
We show that in a rank supersolvable lattice that is graded by a bounded real interval, any antichain cutset is a level set for some appropriately constructed grading. As a consequence, given an antichain cutset in any of the measurable Boolean lattice, a continuous partition lattice, or a continuous projective geometry, we may find a grading in which the cutset is a level set.
- Denys Bulavka and Russ Woodroofe, Strict Erdős-Ko-Rado theorems for simplicial complexes, preprint.
We show that if a simplicial complex is a near-cone of sufficiently high depth, then the only maximum families of small pairwise intersecting faces are those with a common intersection. Thus, near-cones of sufficiently high depth satisfy the strict Erdős-Ko-Rado property conjectured by Holroyd and Talbot and by Borg. One consequence is a strict Erdős-Ko-Rado theorem for independence complexes of chordal graphs with an isolated vertex. Under stronger shiftedness conditions, we prove a sharper stability theorem of Hilton-Milner type, as well as two cross-intersecting theorems.