Journal article
Fixing a hole
- Abstract:
- We show that any finite S⊂ Rd in general position has arbitrarily large supersets T⊇ S in general position with the property that T contains no empty convex polytope, or hole, with Cd points, where Cd is an integer that depends only on the dimension d. This generalises results of Horton and Valtr which treat the case S= ∅ . The key step in our proof, which may be of independent interest, is to show that there are arbitrarily small perturbations of the set of lattice points [n] d with no large holes.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
Actions
Access Document
- Files:
-
-
(Preview, Accepted manuscript, pdf, 362.6KB, Terms of use)
-
- Publisher copy:
- 10.1007/s00454-023-00561-6
Authors
+ Directorate for Mathematical and Physical Sciences
More from this funder
- Funder identifier:
- https://ror.org/029b7h395
- Publisher:
- Springer
- Journal:
- Discrete and Computational Geometry More from this journal
- Volume:
- 70
- Issue:
- 4
- Pages:
- 1551-1570
- Publication date:
- 2023-09-07
- Acceptance date:
- 2023-03-25
- DOI:
- EISSN:
-
1432-0444
- ISSN:
-
0179-5376
- Language:
-
English
- Keywords:
- Pubs id:
-
1528687
- Local pid:
-
pubs:1528687
- Deposit date:
-
2025-12-26
- ARK identifier:
Terms of use
- Copyright holder:
- Conlon et al.
- Copyright date:
- 2023
- Rights statement:
- Copyright © 2023, The Author(s), under exclusive licence to Springer Science Business Media, LLC, part of Springer Nature
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Springer at https://dx.doi.org/10.1007/s00454-023-00561-6
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