Speaker
Rick Danner
(University of Vermont)
Description
Building sets were introduced in the study of wonderful compactifications
of hyperplane arrangement complements and were later generalized to finite meet-
semilattices. Convex geometries, the duals of antimatroids, offer a robust combinatorial
abstraction of convexity. Supersolvable convex geometries and antimatroids appear in
the study of poset closure operators, Coxeter groups, and matroid activities. We prove
that the building sets on a finite meet-semilattice form a supersolvable convex geometry.
As an application, we demonstrate that building sets and nested set complexes respect
certain restrictions of finite meet-semilattices unifying and extending results of several
authors.
Primary author
Rick Danner
(University of Vermont)
