3 citations · 8 across the 12 of their papers we have counts for
5 papers · 1 filter
A Polytopal Realization of Higher-Categorical Associahedra
Spencer Backman, Nathaniel Bottman, Daria Poliakova
We describe a polytopal realization of categorical -associahedra. The normal fan of this polytopal realization is a modification of the authors' velocity fan and was found by Op…
More (shifted) runners, less loneliness
Daria Poliakova
The shifted lonely runner conjecture was recently disproved by Blanco, Criado and Santos. We give quantitative bounds on its failure as the number of runners grows. The loneliness…
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…