Discrete Morse theory for moduli spaces of flexible polygons, or solitaire game on the circle

Panina, Gaiane; Zhukova, Alena

doi:10.48550/arxiv.1504.05139

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2016

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“…(2) Theorem 2 is proven via discrete Morse theory by R. Forman [1]. In a sense, it is a simplification of the approach of [5] where a perfect discrete Morse function on the moduli space of a polygonal linkage was constructed.…”

Section: Introductionmentioning

confidence: 99%

Cyclopermutohedron: geometry and topology

Nekrasov

Panina

Zhukova

2016

European Journal of Mathematics

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The face poset of the permutohedron realizes the combinatorics of linearly ordered partitions of the set [n] = {1, . . . , n}. Similarly, the cyclopermutohedron is a virtual polytope that realizes the combinatorics of cyclically ordered partitions of the set [n + 1]. The cyclopermutohedron was introduced by the second author by motivations coming from configuration spaces of polygonal linkages. In the paper we prove two facts: (a) the volume of the cyclopermutohedron equals zero, and (b) the homology groups H k for k = 0, . . . , n −2 of the face poset of the cyclopermutohedron are non-zero free abelian groups. We also present a short formula for their ranks.

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Section: Introductionmentioning

confidence: 99%