ADDITIVE COMPLEMENTS FOR A GIVEN ASYMPTOTIC DENSITY
| Autor: | Ram Krishna Pandey, Alain Faisant, Georges Grekos, Sai Teja Somu |
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| Přispěvatelé: | Combinatoire, théorie des nombres (CTN), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Grekos, Georges |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Mathematics - Number Theory
General Mathematics 010102 general mathematics Sumset 01 natural sciences [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] 010101 applied mathematics Combinatorics Integer FOS: Mathematics Natural density Number Theory (math.NT) 0101 mathematics Mathematics [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT] |
| Popis: | {The first version of this text was written and submitted to a journal on April, 12, 2018. This second version was submitted on April, 9, 2019.} We investigate the existence of subsets $A$ and $B$ of $\mathbb{N}:=\{0,1,2,\dots\}$ such that the sumset $A+B:=\{a+b~;a\in A,b\in B\}$ has given asymptotic density. We solve the particular case in which $B$ is a given finite subset of $\mathbb{N}$ and also the case when $B=A$ ; in the later case, we generalize our result to $kA:=\{x_1+\cdots+x_k: x_i\in A, i=1,\dots,k\}$ for an integer $k\geq2.$ Comment: 13 pages |
| Databáze: | OpenAIRE |
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