On the multiplicity of arrangements of congruent zones on the sphere

[1705.02172] On the multiplicity of arrangements of congruent zones on the sphere Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Metric Geometry arXiv:1705.02172 (math) [Submitted on 5 May 2017 ( v1 ), last revised 6 Oct 2023 (this version, v3)] Title: On the multiplicity of arrangements of congruent zones on the sphere Authors: A. Bezdek , F. Fodor , V. Vígh , T. Zarnócz View a PDF of the paper titled On the multiplicity of arrangements of congruent zones on the sphere, by A. Bezdek and 3 other authors View PDF HTML (experimental) Abstract: Consider an arrangement of $n$ congruent zones on the $d$-dimensional unit sphere $S^{d-1}$, where a zone is the intersection of an origin symmetric Euclidean plank with $S^{d-1}$. We prove that, for sufficiently large $n$, it is possible to arrange $n$ congruent zones of suitable width on $S^{d-1}$ such that no point belongs to more than a constant number of zones, where the constant depends only on the dimension and the width of the zones. Furthermore, we also show that it is possible to cover $S^{d-1}$ by $n$ congruent zones such that each point of $S^{d-1}$ belongs to at most $A_d\ln n$ zones, where the $A_d$ is a constant that depends only on $d$. This extends the corresponding $3$-dimensional result of Frankl, Nagy and Naszódi (2016). Moreover, we also examine coverings of $S^{d-1}$ with congruent zones under the condition that each point of the sphere belongs to the interior of at most $d-1$ zones. Subjects: Metric Geometry (math.MG) MSC classes: 52C17 Cite as: arXiv:1705.02172 [math.MG] (or arXiv:1705.02172v3 [math.MG] for this version) https://doi.org/10.48550/arXiv.1705.02172 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Studia Sci. Math. Hungar. 61, No. 3, (2024), 262-273 Related DOI : https://doi.org/10.1556/012.2024.04319 Focus to learn more DOI(s) linking to related resources Submission history From: Ferenc Fodor [ view email ] [v1] Fri, 5 May 2017 11:28:02 UTC (11 KB) [v2] Thu, 6 Jun 2019 12:53:22 UTC (11 KB) [v3] Fri, 6 Oct 2023 11:19:12 UTC (15 KB) Full-text links: Access Paper: View a PDF of the paper titled On the multiplicity of arrangements of congruent zones on the sphere, by A. Bezdek and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.MG < prev | next > new | recent | 2017-05 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

Related documents

• Isospectral orbifolds with different isotropy orders#641995
• Galois-theoretic Characterization of Geometric Isomorphism Classes of Quasi-monodromically Full Hyperbolic Curves with Small Numerical Invariants#436447
• Galois-theoretic Characterization of Geometric Isomorphism Classes of Quasi-monodromically Full Hyperbolic Curves with Small Numerical Invariants#436442
• Gromov-Witten theory of abelian varieties in families and modular forms#625296
• Gromov-Witten theory of abelian varieties in families and modular forms#623023