An Erdös–Fuchs theorem for ordered representation functions
| Autor: | Christoph Spiegel, Gonzalo Cao-Labora, Juanjo Rué |
|---|---|
| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics |
| Rok vydání: | 2020 |
| Předmět: |
Algebra and Number Theory
Mathematics - Number Theory Star (game theory) 010102 general mathematics Matemàtiques i estadística [Àrees temàtiques de la UPC] Additive Number Theory 0102 computer and information sciences 01 natural sciences Combinatorics additive basis Number theory Erdös-Fuchs Theorem Integer 010201 computation theory & mathematics Additive number theory representation functions Mathematics - Combinatorics 11 Number theory::11B Sequences and sets [Classificació AMS] 0101 mathematics Mathematics |
| Zdroj: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Popis: | Let $k\geq 2$ be a positive integer. We study concentration results for the ordered representation functions $r^{\leq}_k(A,n) = \# \big\{ (a_1 \leq \dots \leq a_k) \in A^k : a_1+\dots+a_k = n \big\}$ and $r^{ 0$ and $\star \in \{\leq,0$. These results extend two theorems for the non-ordered representation function proved by Erd\H{o}s and Fuchs in the case of $k=2$ (J. of the London Math. Society 1956). Comment: 15 pages |
| Databáze: | OpenAIRE |
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