Transformations of lattice diagrams and their associated dotted diagrams

[2310.00218] Transformations of lattice diagrams and their associated dotted diagrams Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Geometric Topology arXiv:2310.00218 (math) [Submitted on 30 Sep 2023 ( v1 ), last revised 3 May 2025 (this version, v2)] Title: Transformations of lattice diagrams and their associated dotted diagrams Authors: Inasa Nakamura View a PDF of the paper titled Transformations of lattice diagrams and their associated dotted diagrams, by Inasa Nakamura View PDF HTML (experimental) Abstract: We consider a graph called a lattice diagram, which is a graph in the $xy$-plane such that each edge is parallel to the $x$-axis or the $y$-axis. In [4], we investigated transformations of certain lattice diagrams, and we considered the reduced diagram that is obtained from deformations of a diagram associated with a lattice diagram. In this paper, we refine the notion of the reduced diagram by introducing the notion of a dotted diagram. A lattice diagram is presented by an admissible dotted diagram. We investigate deformations of dotted diagrams, and we investigate relation between deformations of admissible dotted diagrams and transformations of lattice diagrams, giving results that are refined and corrected versions of [4, Lemma 6.2, Theorem 6.3]. Comments: 25 pages, 13 figures, title changed, Definition this http URL revised, to appear in Kyungpoook Math. J Subjects: Geometric Topology (math.GT) Cite as: arXiv:2310.00218 [math.GT] (or arXiv:2310.00218v2 [math.GT] for this version) https://doi.org/10.48550/arXiv.2310.00218 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Kyungpook Math. J. 65(2025), 331-356 Related DOI : https://doi.org/10.5666/KMJ.2025.65.2.331 Focus to learn more DOI(s) linking to related resources Submission history From: Inasa Nakamura [ view email ] [v1] Sat, 30 Sep 2023 01:46:54 UTC (926 KB) [v2] Sat, 3 May 2025 23:43:02 UTC (859 KB) Full-text links: Access Paper: View a PDF of the paper titled Transformations of lattice diagrams and their associated dotted diagrams, by Inasa Nakamura View PDF HTML (experimental) TeX Source view license Current browse context: math.GT < prev | next > new | recent | 2023-10 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs 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? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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