• Corpus ID: 118366413

Volume and lattice points counting for the cyclopermutohedron

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

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