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On the Covering Densities of Quarter-Convex Disks

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Abstract

It is conjectured that for every convex disk \(K\), the translative covering density of \(K\) and the lattice covering density of \(K\) are identical. It is well known that this conjecture is true for every centrally symmetric convex disk. For the non-symmetric case, we only know that the conjecture is true for triangles (Januszewski in Discrete Comput Geom 43:167–178, 2010). In this paper, we prove the conjecture for a class of convex disks (quarter-convex disks), which includes all triangles and convex quadrilaterals.

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Acknowledgments

This work was supported by 973 Programs 2013CB834201 and 2011CB302401.

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Authors and Affiliations

  1. Peking University, Beijing, China

    Kirati Sriamorn & Fei Xue

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  1. Kirati Sriamorn
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  2. Fei Xue
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Correspondence to Kirati Sriamorn.

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Editor in charge: János Pach.

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Sriamorn, K., Xue, F. On the Covering Densities of Quarter-Convex Disks. Discrete Comput Geom 54, 246–258 (2015). https://doi.org/10.1007/s00454-015-9696-8

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  • DOI: https://doi.org/10.1007/s00454-015-9696-8

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