On strong infinite Sidon and Bh sets and random sets of integers
| Autor: | Juanjo Rué, David Fabian, Christoph Spiegel |
|---|---|
| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Extremal combinatorics
Additive combinatorics 05 Combinatorics [Classificació AMS] Matemàtiques i estadística [Àrees temàtiques de la UPC] Probabilistic combinatorics Measure (mathematics) Upper and lower bounds Theoretical Computer Science Set (abstract data type) Combinatorics Random sets Computational Theory and Mathematics Discrete Mathematics and Combinatorics Mathematics |
| Zdroj: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| DOI: | 10.1016/j.jcta.2021.105460 |
| Popis: | A set of integers S ⊂ N is an α–strong Sidon set if the pairwise sums of its elements are far apart by a certain measure depending on α, more specifically if | ( x + w ) − ( y + z ) | ≥ max { x α , y α , z α , w α } for every x , y , z , w ∈ S satisfying max { x , w } ≠ max { y , z } . We obtain a new lower bound for the growth of α–strong infinite Sidon sets when 0 ≤ α 1 . We also further extend that notion in a natural way by obtaining the first non-trivial bound for α–strong infinite B h sets. In both cases, we study the implications of these bounds for the density of, respectively, the largest Sidon or B h set contained in a random infinite subset of N . Our theorems improve on previous results by Kohayakawa, Lee, Moreira and Rodl. |
| Databáze: | OpenAIRE |
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