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.
Originalsprache | englisch |
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Seiten (von - bis) | 43–65 |
Seitenumfang | 23 |
Fachzeitschrift | Annals of Combinatorics |
Jahrgang | 28 |
Ausgabenummer | 1 |
Frühes Online-Datum | 19 Mai 2023 |
DOIs | |
Publikationsstatus | Veröffentlicht - März 2024 |
ASJC Scopus subject areas
- Diskrete Mathematik und Kombinatorik