Séminaire Lotharingien de Combinatoire, 91B.28 (2024), 12 pp.
Chiara Mantovani, Arnau Padrol and Vincent Pilaud
Acyclonestohedra
Abstract.
Given a building set B and an oriented matroid M on the
same ground set, we define the acyclic nested complex as the
simplicial complex of nested sets on B which are in some
sense acyclic with respect to M.
We prove that this complex is always the face lattice of an oriented
matroid, obtained as a stellar subdivision of the positive tope of the
oriented matroid M.
When the oriented matroid M is the oriented matroid of a vector
configuration A, we moreover prove that this complex is the
boundary complex of an acyclonestohedron, a polytope obtained as the
section of a nestohedron for B by the evaluation space
of A.
Our work specializes to explicit polytopal realizations of the poset
associahedra and affine poset cyclohedra of Galashin.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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