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math.MG2016
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…
math.MG2010
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…