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:2203.00643 (math)
[Submitted on 1 Mar 2022]

Title:A Lattice-Theoretic Perspective on the Persistence Map

Authors:Brendan Mallery, Adélie Garin, Justin Curry
View PDF
Abstract:We provide a naturally isomorphic description of the persistence map from merge trees to barcodes in terms of a monotone map from the partition lattice to the subset lattice. Our description is local, which offers the potential to speed up inverse computations, and brings classical tools in combinatorics to bear on an active area of research in topological data analysis (TDA).
Comments: 4 pages, 2 figures
Subjects: Algebraic Topology (math.AT); Computational Geometry (cs.CG); Combinatorics (math.CO)
Cite as: arXiv:2203.00643 [math.AT]
  (or arXiv:2203.00643v1 [math.AT] for this version)
  https://doi.org/10.48550/arXiv.2203.00643

Submission history

From: Justin Curry [view email]
[v1] Tue, 1 Mar 2022 17:35:27 UTC (254 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
license icon view license
Current browse context:
math.AT
< prev   |   next >
new | recent | 2022-03
Change to browse by:
cs
cs.CG
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?)