Comparing Diagonals on the Associahedra
Algebraic Topology
2024-02-26 v4 Combinatorics
Abstract
We prove that the formula for the diagonal approximation on J. Stasheff's -dimensional associahedron derived by the current authors in 2004 agrees with the "magical formula" for the diagonal approximation derived by Markl and Shnider in 2006, by Loday in 2011, and by Masuda, Thomas, Tonks, and Vallette in 2021.
Cite
@article{arxiv.2207.08543,
title = {Comparing Diagonals on the Associahedra},
author = {Samson Saneblidze and Ronald Umble},
journal= {arXiv preprint arXiv:2207.08543},
year = {2024}
}
Comments
The initial posting defines the S-U diagonal $\Delta_K$ on the top dimensional cell of $K_n$; its value on proper faces is given by comultiplicative extension. Version 2 defines $\Delta_K$ on all faces of $K_n$ explicitly. Version 3 incorporates recommendations by the referee. Version 4 cites a paper by Loday. 8 pages, 3 Figures