Bulletin of the Australian Mathematical
Society
Bull. Austral. Math. Soc.
0004-9727
ALNBAB
2005
72
1
10.wxyz/CV72P1
http://www.austms.org.au/Publ/Bulletin/V72P1/
On the monotonicity properties of additive
representation functions
Yong-Gao Chen
András Sárközy
Vera T. Sós
Min Tang
14 February 2006
2006
2
14
129
138
721-5098-ChSaSoMi-2005
10.wxyz/C2005V72P1p129
http://www.austms.org.au/Publ/Bulletin/V72P1/721-5098-ChSaSoMi/
If $A$ is a set of positive integers, let $R_{1}
(n)$ be the number of solutions of $a+a' = n $, $a$, $a'\in
A$, and let $R_{2}(n)$ and $R_{3}(n)$ denote the number of
solutions with the additional restrictions $a < a'$, and
$a\leq a'$ respectively. The monotonicity properties of the
three functions $R_{1}(n)$, $R_{2}(n)$, and $R_{3}(n)$ are
studied and compared.
11B34
MR2162298
02212190
Research supported by the NSF of China Grant
10471064, the SF of AnHui Province Grant 01046103 and the
Hungarian National Foundation for Scientific Research Grant
T043623, T042750, T038210, T046378.
M. Ajtai, J. Komlós and E. Szemerédi
A dense infinite Sidon
sequence
European J. Combin.
MR611925
M. Ajtai, J.
Koml\'{o}s and E. Szemer\'{e}di; A dense infinite Sidon
sequence, \textit{European J. Combin.} \textbf{2} (1981),
pp.~1--11.
R. Balasubramanian
A note on a result of Erdős,
Sárközy and Sós
Acta Arith.
MR913763
R. Balasubramanian; A
note on a result of Erd\H{o}s, S\'{a}rk\"{o}zy and S\'{o}s,
\textit{Acta Arith.} \textbf{49} (1987),
pp.~45--53.
P. Erdős, A. Sárközy and V.T. Sós
Problems and
results on additive properties of general sequences,
IV,
Number
Theory, Proceedings, Ootacamund, India, 1984
Lecture Notes in Mathematics
1122
Springer-Verlag
MR797782
P. Erd\H{o}s, A.
S\'{a}rk\"{o}zy and V.T. S\'{o}s; Problems and results on
additive properties of general sequences, IV,, in
\textit{Number Theory, Proceedings, Ootacamund, India,
1984}, Lecture Notes in Mathematics 1122 (Springer-Verlag,
Berlin, 1985), pp.~85--104.
P. Erdős, A. Sárközy and V.T. Sós
Problems and results on additive
properties of general sequences, V
Monatsh. Math.
MR863216
P. Erd\H{o}s, A.
S\'{a}rk\"{o}zy and V.T. S\'{o}s; Problems and results on
additive properties of general sequences, V,
\textit{Monatsh. Math.} \textbf{102} (1986),
pp.~183--197.
P. Erdős, A. Sárközy and V.T. Sós
On additive properties of general
sequences
Discrete Math.
MR1313282
P. Erd\H{o}s, A.
S\'{a}rk\"{o}zy and V.T. S\'{o}s; On additive properties of
general sequences, \textit{Discrete Math.} \textbf{136}
(1994), pp.~75--99.
M. Tang and Y.G. Chen
On additive properties of general
sequences
Bull. Austral. Math. Soc.
MR2150937
M. Tang and Y.G. Chen;
On additive properties of general sequences, \textit{Bull.
Austral. Math. Soc.} \textbf{71} (2005),
pp.~479--485.