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Let $A$ be a finite set of integers. For any integer $h\geq 1$, let $h$-fold sumset $hA$ be the set of all sums of $h$ elements of $A$ and let $h$-fold restricted sumset $h^{\wedge}A$ be the set of all sums of $h$ distinct elements of $A$. In this paper, we give a survey of problems and results on sumsets and restricted sumsets of a finite integer set. In details, we give the best lower bound for the cardinality of restricted sumsets $2^{\wedge}A$ and $3^{\wedge}A$ and also discuss the cardinality of restricted sumset $h^{\wedge}A$.
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참고문헌 (15)
참고문헌 신청
J. Bhanja / 2017 / Counting the number of elements in h(r)A : A special case / J. Combin. Number Theory 9:215~227
G. A. Freiman / 1959 / The addition of nite sets. I / Izv. Vyss. Ucebn. Zaved. Matematika (6):202~213
G. A. Freiman / 1962 / Inverse problems of additive number theory. VI. On the addition of nite sets. III / Izv. VysS. Ucebn. Zaved. Matematika 1962(3):151~157
G. A. Freiman / 1999 / Sumsets with distinct summands and the Erd}os-Heilbronn conjecture on sums of residues / Asterisque (258):163~172
V. F. Lev / 1996 / Structure theorem for multiple addition and the Frobenius problem / J. Number Theory 58(1):79~88
G. A. Freiman / 1959 / The addition of nite sets. I / Izv. Vyss. Ucebn. Zaved. Matematika (6):202~213
G. A. Freiman / 1962 / Inverse problems of additive number theory. VI. On the addition of nite sets. III / Izv. VysS. Ucebn. Zaved. Matematika 1962(3):151~157
G. A. Freiman / 1999 / Sumsets with distinct summands and the Erd}os-Heilbronn conjecture on sums of residues / Asterisque (258):163~172
V. F. Lev / 1996 / Structure theorem for multiple addition and the Frobenius problem / J. Number Theory 58(1):79~88
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