- Title
- Midpoint-free subsets of the real numbers
- Creator
- Eggleton, Roger B.
- Relation
- International Journal of Combinatorics Vol. 2014
- Publisher Link
- http://dx.doi.org/10.1155/2014/214637
- Publisher
- Hindawi
- Resource Type
- journal article
- Date
- 2014
- Description
- A set of reals 𝑆 ⊂ R is midpoint-free if it has no subset {𝑎, 𝑏, 𝑐} ⊆ 𝑆 such that 𝑎<𝑏<𝑐 and 𝑎 + 𝑐 = 2𝑏. If 𝑆 ⊂ 𝑋 ⊆ R and 𝑆 is midpoint-free, it is a maximal midpoint-free subset of 𝑋 if there is no midpoint-free set 𝑇 such that 𝑆 ⊂ 𝑇 ⊆ 𝑋. In each of the cases 𝑋 = Z+, Z, Q+, Q, R+, R, we determine two maximal midpoint-free subsets of 𝑋 characterised by digit constraints on the base 3 representations of their members.
- Subject
- midpoint-free; real numbers; combinatorics
- Identifier
- http://hdl.handle.net/1959.13/1296220
- Identifier
- uon:19218
- Identifier
- ISSN:1687-9163
- Language
- eng
- Full Text
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