Self-similarity and the transition from finite to infinite measures in dynamical s...
On the unit group of Z-orders in finite dimensional algebras
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| Author(s): |
Total Authors: 4
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| Affiliation: | [1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo - Brazil
[2] Duksung Womens Univ, Dept Math, Seoul 01369 - South Korea
[3] IMPA, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro - Brazil
[4] Emory Univ, Dept Math & Comp Sci, Atlanta, GA 30322 - USA
Total Affiliations: 4
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| Document type: | Journal article |
| Source: | SIAM JOURNAL ON DISCRETE MATHEMATICS; v. 32, n. 1, p. 410-449, 2018. |
| Web of Science Citations: | 0 |
| Abstract | |
A set S of natural numbers is a Sidon set if all the sums s(1) + s(2) with s(1), s(2) epsilon S and s(1) <= s(2) are distinct. Let constants alpha > 0 and 0 < delta < 1 be fixed, and let p(m) = min[1, alpha m (1 vertical bar delta)] for all positive integers m. Generate a random set R subset of N by adding m to R with probability p(m), independently for each m. We investigate how dense a Sidon set S contained in R can be. Our results show that the answer is qualitatively very different in at least three ranges of delta. We prove quite accurate results for the range 0 < delta <= 2/3, but only obtain partial results for the range 2/3 < delta <= 1. (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 |
| FAPESP's process: | 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat |
| Grantee: | Oswaldo Baffa Filho |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |