2 citations · 4 across the 4 of their papers we have counts for
5 papers
Intersection numbers of Chern classes of tautological line bundles on the moduli spaces of flexible polygons
Ilia Nekrasov, Gaiane Panina, Alena Zhukova
Given a flexible -gon with generic side lengths, the moduli space of its configurations in as well as in is a smooth manifold. It is equipped with…
Discrete Morse theory for the barycentric subdivision
A. M Zhukova
Let be a discrete Morse function on a simplicial complex . We construct a discrete Morse function on the barycentric subdivision . The constructed function $Δ(F…
Cyclopermutohedron: geometry and topology
Ilia Nekrasov, Gaiane Panina, Alena Zhukova
The face poset of the permutohedron realizes the combinatorics of linearly ordered partitions of the set . Similarly, the cyclopermutohedron is a virtual polytope…
Discrete Morse theory for moduli spaces of flexible polygons, or solitaire game on the circle
Gaiane Panina, Alena Zhukova
We introduce a perfect discrete Morse function on the moduli space of a polygonal linkage. The ingredients of the construction are: (1) the cell structure on the moduli space, and…
Morse index of a cyclic polygon
Gaiane Panina, Alena Zhukova
It is known that cyclic configurations of a planar polygonal linkage are critical points of the signed area function. In the paper, we announce an explicit formula of the Morse ind…