Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Algebraic Topology

arXiv:2207.08543 (math)
[Submitted on 18 Jul 2022 (v1), last revised 23 Feb 2024 (this version, v4)]

Title:Comparing Diagonals on the Associahedra

Authors:Samson Saneblidze, Ronald Umble
View PDF HTML (experimental)
Abstract:We prove that the formula for the diagonal approximation $\Delta_{K}$ on J. Stasheff's $n$-dimensional associahedron $K_{n+2}$ derived by the current authors in 2004 agrees with the "magical formula" for the diagonal approximation $\Delta_{K}^{\prime}$ derived by Markl and Shnider in 2006, by Loday in 2011, and by Masuda, Thomas, Tonks, and Vallette in 2021.
Comments: The initial posting defines the S-U diagonal $Δ_K$ on the top dimensional cell of $K_n$; its value on proper faces is given by comultiplicative extension. Version 2 defines $Δ_K$ 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
Subjects: Algebraic Topology (math.AT); Combinatorics (math.CO)
MSC classes: Primary 55P48, 55P99, Secondary 52B05, 52B11
Cite as: arXiv:2207.08543 [math.AT]
  (or arXiv:2207.08543v4 [math.AT] for this version)
  https://doi.org/10.48550/arXiv.2207.08543

Submission history

From: Ronald Umble [view email]
[v1] Mon, 18 Jul 2022 12:08:26 UTC (10 KB)
[v2] Wed, 3 Aug 2022 18:43:37 UTC (10 KB)
[v3] Mon, 9 Oct 2023 13:03:44 UTC (10 KB)
[v4] Fri, 23 Feb 2024 16:59:04 UTC (11 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.AT
< prev   |   next >
new | recent | 2022-07
Change to browse by:
math
math.CO

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)