NDLI: Cyclopermutohedron

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Improvements of the Frankl-Rödl theorem on the number of edges of a hypergraph with forbidden intersections, and their consequences in the problem of finding the chromatic number of a space with forbidden equilateral triangle

Local approach and the theory of lovozerite structures

Extremal problems of circle packings on a sphere and irreducible contact graphs

Cyclopermutohedron

On a higher dimensional generalization of Seifert fibrations

On flexible polyhedral surfaces

Ergodic properties of visible lattice points

A survey on tight Euclidean t-designs and tight relative t-designs in certain association schemes

(n,m)-fold covers of spheres

Density bounds for outer parallel domains of unit ball packings

Cube-like incidence complexes and their groups

New results on torus cube packings and tilings

Inductive rotation tilings

Delaunay sets and condensed matter: The dialogue continues

Correction to the paper “Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source” (Proc. Steklov Inst. Math. 281, 161–178 (2013))

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Cyclopermutohedron

Content Provider	Springer Nature Link
Author	Panina, Gaiane Yu.
Copyright Year	2015
Abstract	It is well known that the k-faces of the permutohedron Π$_{ n }$ can be labeled by (all possible) linearly ordered partitions of the set [n] = {1,..., n} into n − k nonempty parts. The incidence relation corresponds to the refinement: a face F contains a face F′ whenever the label of F′ refines the label of F. We consider the cell complex CP$_{ n+1}$ defined in a similar way but with the linear ordering replaced by the cyclic ordering. Namely, the k-cells of the complex CP$_{ n+1}$ are labeled by (all possible) cyclically ordered partitions of the set [n + 1] = {1,..., n + 1} into n + 1 − k > 2 nonempty parts. The incidence relation in CP$_{ n+1}$ again corresponds to the refinement: a cell F contains a cell F′ whenever the label of F′ refines the label of F. The complex CP$_{ n+1}$ cannot be represented by a convex polytope, since it is not a combinatorial sphere (not even a combinatorial manifold). However, it can be represented by some virtual polytope (that is, the Minkowski difference of two convex polytopes), which we call a cyclopermutohedron CP $_{ n+1}$. It is defined explicitly as a weighted Minkowski sum of line segments. Informally, the cyclopermutohedron can be viewed as a “permutohedron with diagonals.” One of the motivations for introducing such an object is that the cyclopermutohedron is a “universal” polytope for moduli spaces of polygonal linkages.
Starting Page	132
Ending Page	144
Page Count	13
File Format	PDF
ISSN	00815438
Journal	Proceedings of the Steklov Institute of Mathematics
Volume Number	288
Issue Number	1
e-ISSN	15318605
Language	English
Publisher	Pleiades Publishing
Publisher Date	2015-05-01
Publisher Place	Moscow
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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