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