3 citations · 8 across the 12 of their papers we have counts for
14 papers
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…
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…
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…
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…
Constrainahedra
Nathaniel Bottman, Daria Poliakova
We define a family of convex polytopes called constrainahedra, which index collisions of horizontal and vertical lines. Our construction proceeds by first defining a poset …
Freehedra are short
Daria Poliakova
We prove the combinatorial property of shortness for freehedra. Note that associahedra, a sibling family of polytopes, are not short.
From polytopes to operads and back
Sergey Arkhipov, Daria Poliakova
For a directed polytope, we construct a colored operad whose Poincare-Hilbert series encodes certain operations on the cellular complex of the polytope. We conjecture that for a cl…
Cellular chains on freehedra and operadic pairs
Daria Poliakova
The paper is devoted to explaining the operadic meaning of freehedra, a family of polytopes originally defined to study free loop spaces. We introduce the notion of operadic pairs…
Homotopy characters as a homotopy limit
Sergey Arkhipov, Daria Poliakova
For a Hopf DG-algebra corresponding to a derived algebraic group, we compute the homotopy limit of the associated cosimplicial system of DG-algebras given by the classifying space…
A note on a Holstein construction
Sergey Arkhipov, Daria Poliakova
We clarify details and fill certain gaps in the construction of a canonical Reedy fibrant resolution for a constant simplicial DG-category due to Holstein.