The restricted sumsets in ℤ_n

2018/10/12 by Tang, Min, Wei, Meng-Ting
#11B13 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1810.05346

Abstract

Let h≥ 2 be a positive integer. For any subset A⊂ ℤ_n, let h^\wedgeA be the set of the elements of ℤ_n which are sums of h distinct elements of A. In this paper, we obtain some new results on 4^\wedgeA and 5^\wedgeA. For example, we show that if |A|≥ 0.4045n and n is odd, then 4^\wedgeA=ℤ_n; Under some conditions, if n is even and |A| is close to n/4, then 4^\wedgeA=ℤ_n.

Related

• Extended inverse results for restricted h-fold sumset in integers
• Restricted sumsets in ℤ
• Bounds on the cardinality of restricted sumsets in ℤ_p
• Sumsets with a minimum number of distinct terms
• The restricted sumsets in finite abelian groups