Abstract
The polytopes UI,J¯ were introduced by Ceballos, Padrol, and Sarmiento to provide a geometric approach to the study of (I,J¯)-Tamari lattices. They observed a connection between certain UI,J¯ and acyclic root polytopes, and wondered if Mészáros’ subdivision algebra can be used to subdivide all UI,J¯. We answer this in the affirmative from two perspectives, one using flow polytopes and the other using root polytopes. We show that UI,J¯ is integrally equivalent to a flow polytope that can be subdivided using the subdivision algebra. Alternatively, we find a suitable projection of UI,J¯ to an acyclic root polytope which allows subdivisions of the root polytope to be lifted back to UI,J¯. As a consequence, this implies that subdivisions of UI,J¯ can be obtained with the algebraic interpretation of using reduced forms of monomials in the subdivision algebra. In addition, we show that the (I,J¯)-Tamari complex can be obtained as a triangulated flow polytope.
Original language | English |
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Pages (from-to) | 43-65 |
Number of pages | 23 |
Journal | Annals of Combinatorics |
Volume | 28 |
Issue number | 1 |
DOIs | |
State | Published - Mar 2024 |
Bibliographical note
Publisher Copyright:© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics