| Full text | |
| Author(s): |
Total Authors: 4
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| Affiliation: | [1] Eotvos Lorand Univ, Inst Math, Pazmany P Setany 1-C, H-1117 Budapest - Hungary
[2] Hungarian Acad Sci, Alfred Renyi Inst Math, POB 127, H-1364 Budapest - Hungary
[3] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | DISCRETE & COMPUTATIONAL GEOMETRY; v. 55, n. 3, p. 642-661, APR 2016. |
| Web of Science Citations: | 0 |
| Abstract | |
A 1-avoiding set is a subset of that does not contain pairs of points at distance 1. Let denote the maximum fraction of that can be covered by a measurable 1-avoiding set. We prove two results. First, we show that any 1-avoiding set in that displays block structure (i.e., is made up of blocks such that the distance between any two points from the same block is less than 1 and points from distinct blocks lie farther than 1 unit of distance apart from each other) has density strictly less than . For the special case of sets with block structure this proves a conjecture of ErdAs asserting that . Second, we use linear programming and harmonic analysis to show that m(1) (R-2) <= 0.258795. (AU) | |
| FAPESP's process: | 13/03447-6 - Combinatorial structures, optimization, and algorithms in theoretical Computer Science |
| Grantee: | Carlos Eduardo Ferreira |
| Support Opportunities: | Research Projects - Thematic Grants |