On the Subdivision Algebra for the Polytope UI,

Matias von Bell, Martha Yip

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 languageEnglish
Pages (from-to)43-65
Number of pages23
JournalAnnals of Combinatorics
Volume28
Issue number1
DOIs
StatePublished - 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

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