4 papers
Stability and ribbon bases for the rank-selected homology of geometric lattices
Patricia Hersh, Sheila Sundaram
This paper analyzes the representation theoretic stability, in the sense of Thomas Church and Benson Farb, of the rank-selected homology of the Boolean lattice and the partition la…
Poset topology, moves, and Bruhat interval polytope lattices
Christian Gaetz, Patricia Hersh
We study the poset topology of lattices arising from orientations of 1-skeleta of directionally simple polytopes, with Bruhat interval polytopes as our main example. We s…
Extended Weak Order for the Rank 3 Universal Coxeter Group
Grant Barkley, Colin Defant, Patricia Hersh +3
The weak order is a classical poset structure on a Coxeter group; it is a lattice when the group is finite but merely a meet-semilattice when the group is infinite. Motivated by pr…
Fibers of maps to totally nonnegative spaces
James F. Davis, Patricia Hersh, Ezra Miller
This paper undertakes a study of the structure of the fibers of the Chevalley exponentiation maps . The fibers of these maps encode the…