Labelled Maximal Tubings on Paths and Graph Associahedra

Gürbüzer S. K., Akyar B.

EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, vol.12, no.3, pp.734-748, 2019 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 3
  • Publication Date: 2019
  • Doi Number: 10.29020/nybg.ejpam.v12i3.3448
  • Journal Name: EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.734-748
  • Keywords: Graph associahedra, dendriform algebra, triangulation, realization, REALIZATION
  • Dokuz Eylül University Affiliated: Yes

Abstract

We determine the triangulation of a cyclohedron compatible with the Tamari order on its faces. We define 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 define labelled maximal tubings on paths and give to an application of tubings in homological algebra.