6 papers
Order dimension beyond rank for simplicial hyperplane arrangements
Daria Poliakova
We show that the order dimension of the poset of regions in a simplicial hyperplane arrangement can exceed its rank, answering a question of Reading and Segovia. Examples are Coxet…
Homotopy types of intervals in corank-three higher Bruhat orders
Daria Poliakova
We prove Reiner's conjecture for higher Bruhat orders in corank 3: the facial intervals of B(n,n-3) are precisely the spherical intervals, and all other intervals are contractible.
Lifting Cubic Realizations of Weak Orders in Types A and B
Daria Poliakova
We study cubic realizations of posets compatible with projection maps, meaning that the projection is represented by deletion of the last coordinate. For cylindrical projections, w…
Asymptotic lengths of permutahedra and associahedra
Daria Poliakova
We define asymptotic lengths for families of oriented polytopes. We show that permutahedra with weak order orientations have asymptotic total length 1 and associahedra with Tamari…
Hochschild polytopes
Vincent Pilaud, Daria Poliakova
The -multiplihedron is a polytope whose faces correspond to -painted -trees, and whose oriented skeleton is the Hasse diagram of the rotation lattice on binary -pai…
Higher-Categorical Associahedra
Spencer Backman, Nathaniel Bottman, Daria Poliakova
The second author introduced 2-associahedra as a tool for investigating functoriality properties of Fukaya categories, and he conjectured that they could be realized as face posets…