In this paper, (d + 1)-pencil lattices on simplicial partitions in Rd are studied. The barycentric approach naturally extends the lattice from a simplex to a simplicial partition,...
Abstract We express the generating function for lattice points in a rational polyhedral cone with a simplicial subdivision in terms of multivariate analogues of the h-polynomials o...
We construct CW spheres from the lattices that arise as the closed sets of a convex closure, the meet-distributive lattices. These spheres are nearly polytopal, in the sense that t...
Louis J. Billera, Samuel K. Hsiao, J. Scott Provan
We investigate fast algorithms for changing between the standard basis and an orthogonal basis of idempotents for M¨obius algebras of finite lattices. We show that every lattice...
We prove analogues for sub-posets of the Dowling lattices of the results of Calderbank, Hanlon, and Robinson on homology of sub-posets of the partition lattices. The technical too...