# Volume and lattice points counting for the cyclopermutohedron

@article{Nekrasov2015VolumeAL, title={Volume and lattice points counting for the cyclopermutohedron}, author={I. I. Nekrasov and Gaiane Panina}, journal={arXiv: Metric Geometry}, year={2015} }

The face lattice 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 $[n]$.
It is known that the volume of the standard permutohedron equals the number of trees with $n$ labeled vertices multiplied by $\sqrt{n}$. The number of integer points of the standard permutohedron equals the number of forests on $n$ labeled…

## References

SHOWING 1-10 OF 10 REFERENCES

### Cyclopermutohedron

- MathematicsProceedings of the Steklov Institute of Mathematics
- 2015

It is well known that the k-faces of the permutohedron Πn can be labeled by (all possible) linearly ordered partitions of the set [n] = {1,..., n} into n − k nonempty parts. The incidence relation…

### Homology of planar polygon spaces

- Mathematics
- 2006

In this paper, we study topology of the variety of closed planar n-gons with given side lengths $$l_1, \dots, l_n$$. The moduli space $$M_\ell$$ where $$\ell =(l_1, \dots, l_n)$$, encodes the shapes…

### Lectures on Polytopes

- Mathematics
- 1994

Based on a graduate course given at the Technische Universitat, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The clear and straightforward…

### Newton polyhedra and toroidal varieties

- Mathematics
- 1977

The toroidal compactification (C~0)~f ~ plays the same role as the projective compactification ~ P ~ in the classical case. Toroidal varieties are well known [2, 3]. It is almost as easy to handle…

### Finitely additive measures of virtual polytopes

- St. Petersburg Math. J., Vol. 4, 2
- 1993

### Invitation to Topological Robotics

- Mathematics, Computer ScienceZurich Lectures in Advanced Mathematics
- 2008

### Moduli Space of a Planar Polygonal Linkage: A Combinatorial Description

- Mathematics
- 2012

We describe and study an explicit structure of a regular cell complex $$\mathcal {K}(L)$$K(L) on the moduli space M(L) of a planar polygonal linkage L. The combinatorics is very much related (but not…

### Virtual polytopes and some classical problems

- St. Petersburg Math. J., Vol. 14, 5
- 2003

### Permutohedra

- Associahedra, and Beyond, Int. Math. Res. Not. Vol. 6
- 2009