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Let $h\geq 2$ and $A=\{a_0,a_1,\ldots,a_{k-1}\}$ be a finite set of integers. It is well-known that $\left|hA\right|=hk-h+1$ if and only if $A$ is a $k$-term arithmetic progression. In this paper, we give some nontrivial inverse results of the sets $A$ with some extremal the cardinalities of $hA$.
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참고문헌 (13)
참고문헌 신청
Yong Chen / 1997 / On addition of two sets of integers / Acta Arithmetica 80(1):83~87
G. A. Fre˘ıman / 1959 / The addition of finite sets / I, Izv. Vysˇs. Uˇcebn. Zaved. Matematika 6(13):202~213
G. A. Fre˘ıman / 1962 / Inverse problems of additive number theory. VI. On the addition of finite sets. III / Izv. VysS. Uˇcebn. Zaved. Matematika 3(28):151~157
G. A. Fre˘ıman / 2009 / Combinatorial number theory and additive group theory / Birkh¨auser Verlag :233~239
Gregory A. Freiman / 2009 / Inverse Additive Number Theory. XI. Long arithmetic progressions in sets with small sumsets / Acta Arithmetica 137(4):325~331
G. A. Fre˘ıman / 1959 / The addition of finite sets / I, Izv. Vysˇs. Uˇcebn. Zaved. Matematika 6(13):202~213
G. A. Fre˘ıman / 1962 / Inverse problems of additive number theory. VI. On the addition of finite sets. III / Izv. VysS. Uˇcebn. Zaved. Matematika 3(28):151~157
G. A. Fre˘ıman / 2009 / Combinatorial number theory and additive group theory / Birkh¨auser Verlag :233~239
Gregory A. Freiman / 2009 / Inverse Additive Number Theory. XI. Long arithmetic progressions in sets with small sumsets / Acta Arithmetica 137(4):325~331
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