The permuto-associahedron revisited. (May 2023)

• Record Type: Journal Article
• Authors: Castillo, Federico; Liu, Fu
• Is Part Of: European journal of combinatorics. Volume 110(2023)
• Publication Date: 2023-05
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2023.103706
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: A classic problem connecting algebraic and geometric combinatorics is the realization problem: given a poset, determine whether there exists a polytope whose face lattice is the poset. In 1990s, Kapranov defined a poset as a hybrid between the face poset of a permutohedron and that of an associahedron, and he asked whether this poset is realizable. Shortly after his question was posed, Reiner and Ziegler provided a realization. Based on our previous work on the nested braid fan, we provide in this paper a different realization of Kapranov's poset by constructing the vertex set and the normal fan of a permuto-associahedron simultaneously.