Abstract

PILAUD, Vincent. Which nestohedra are removahedra?. Rev.colomb.mat. [online]. 2017, vol.51, n.1, pp.21-42. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v51n1.66833.

A removahedron is a polytope obtained by deleting inequalities from the facet description of the classical permutahedron. Relevant examples range from the associahedron to the permutahedron itself, which raises the natural question to characterize which nestohedra can be realized as re-movahedra. In this paper, we show that the nested complex of any connected building set closed under intersection can be realized as a removahedron. We present two complementary constructions: one based on the building trees and the nested fan, and the other based on Minkowski sums of dilated faces of the standard simplex. In general, this closure condition is sufficient but not necessary to obtain removahedra. In contrast, we show that the nested fan of a graphical building set is the normal fan of a removahedron if and only if the graphical building set is closed under intersection, which is equivalent to the corresponding graph being chordful (i.e., any cycle induces a clique).

Keywords : Building set; nested complex; nestohedron; graph associahedron; generalized permutahedron; removahedron.

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