Generalized Sidon sets

被引：22

作者：

Cilleruelo, Javier ^{[1
,2
]}

Ruzsa, Imre ^{[3
]}

Vinuesa, Carlos ^{[2
]}

机构：

[1] Univ Autonoma Madrid, Inst Ciencias Matemat CSIC UAM UC3M UCM, E-28049 Madrid, Spain

[2] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

[3] Alfred Renyi Inst Math, H-1364 Budapest, Hungary

来源：

ADVANCES IN MATHEMATICS | 2010年 / 225卷 / 05期

关键词：

Sidon sets; B-2[g] sets; FINITE; NUMBER;

D O I：

10.1016/j.aim.2010.05.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give asymptotic sharp estimates for the cardinality of a set of residue classes with the property that the representation function is bounded by a prescribed number. We then use this to obtain an analogous result for sets of integers, answering an old question of Simon Sidon. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：2786 / 2807

页数：22

共 20 条

[1] Bose R. C., 1942, J. Indian Math. Soc., V6, P1
[2] An upper bound for B2[2] sequences
Cilleruelo, J
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 2000, 89 (01) : 141 - 144
[3] Upper and lower bounds for finite Bh[g] sequences
Cilleruelo, J
Ruzsa, IZ
Trujillo, C
[J]. JOURNAL OF NUMBER THEORY, 2002, 97 (01) : 26 - 34
[4] Sidon sets in Nd
Cilleruelo, Javier
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 2010, 117 (07) : 857 - 871
[5] B2[g] Sets and a Conjecture of Schinzel and Schmidt
Cilleruelo, Javier
Vinuesa, Carlos
[J]. COMBINATORICS PROBABILITY & COMPUTING, 2008, 17 (06) : 741 - 747
[6] Erds P., 1941, J. Lond. Math. Soc, V16, P212, DOI [10.1112/jlms/s1-16.4.212, DOI 10.1112/JLMS/S1-16.4.212]
[7] The number of squares and Bh[g] sets
Green, B
[J]. ACTA ARITHMETICA, 2001, 100 (04) : 365 - 390
[8] HABSIEGER L, 2002, ETAU RESSERRE INTEGE, V2
[9] The density of B-h[g] sequences and the minimum of dense cosine sums
Kolountzakis, MN
[J]. JOURNAL OF NUMBER THEORY, 1996, 56 (01) : 4 - 11
[10] Lindstr??m B., 1969, J COMB THEORY, V6, P211, DOI DOI 10.1016/S0021-9800(69)80124-9

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