English

Equivalence Between Four Models of Associahedra

Combinatorics 2025-11-25 v3 Algebraic Topology

Abstract

We present a combinatorial isomorphism between Stasheff associahedra and an inductive cone construction of those complexes given by Loday. We give an alternate description of certain polytopes, known as multiplihedra, which arise in the study of AA_\infty maps. We also prove a combinatorial isomorphism between Stasheff associahedra, collapsed multiplihedra and graph cubeahedra for path graphs.

Keywords

Cite

@article{arxiv.2201.04847,
  title  = {Equivalence Between Four Models of Associahedra},
  author = {Somnath Basu and Sandip Samanta},
  journal= {arXiv preprint arXiv:2201.04847},
  year   = {2025}
}

Comments

27 pages, 23 figures, some references and figures are added with minor changes, Journal version