Volume and lattice points counting for the cyclopermutohedron
Ilya Nekrasov,
Gaiane Panina
Abstract: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 √ n. The number of integer points of the standard permutohedron equals the number of forests on n labeled vertices.In the paper we prove t… Show more
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