Generalized Sidon sets of perfect powers

作     者：Kiss, Sandor Z. Sandor, Csaba 

作者机构：Budapest Univ Technol & Econ Inst Math Dept Algebra Muegyet Rkp 3 H-1111 Budapest Hungary Budapest Univ Technol & Econ Inst Math Dept Stochast Muegyet Rkp 3 H-1111 Budapest Hungary Budapest Univ Technol & Econ Dept Comp Sci & Informat Theory Muegyet Rkp 3 H-1111 Budapest Hungary ELKH MTA BME Lendulet Arithmet Combinator Res Grp Muegyet Rkp 3 H-1111 Budapest Hungary 

出 版 物：《RAMANUJAN JOURNAL》 (拉马努金杂志)

年 卷 期：2022年第59卷第2期

页      面：351-363页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：National Research, Development and Innovation Office NKFIH [K115288, K129335] Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences New National Excellence Program of the Ministry of Human Capacities [UNKP-18-4] New National Excellence Program of the Ministry for Innovation and Technology [UNKP-19-4] NKFIH [K129335] 

主　　题：Additive number theory General sequences Additive representation function Sidon set 

摘      要：For h = 2 and an infinite set of positive integers A, let R-A,R-h(n) denote the number of representations of the positive integer n as the sum of h distinct terms from A. A set of positive integers A is called a B-h[g] set if every positive integer can be written as the sum of h not necessarily distinct terms from A at most g different ways. We say a set A is a basis of order h if every positive integer can be represented as the sum of h terms from A. Recently, Vu [17] proved the existence of a thin basis of order h formed by perfect powers. In this paper, we study weak B-h[g] sets formed by perfect powers. In particular, we prove the existence of a set A formed by perfect powers with almost possible maximal density such that R-A,R-h(n) is bounded by using probabilistic methods.