Labelled Maximal Tubings on Paths and Graph Associahedra

Sabri Kaan Gürbüzer, Bedia Akyar

Abstract

We determine the triangulation of a cyclohedron compatible with the Tamari order
on its faces. We dene a name of a tubing on a path and a plumbing leading us to construct the dendriform algebra of the collection of maximal tubings on paths. Moreover, we give an operad structure of associahedra and a module structure of cyclohedra via tubings. We dene labelled maximal tubings on paths and give to an application of tubings in homological algebra.

Keywords

Graph associahedra, dendriform algebra, triangulation, realization

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