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A simple proof of a theorem of Bollobás and Leader
Author(s):
Hong
Bing
Yu
Journal:
Proc. Amer. Math. Soc.
131
(2003),
2639-2640.
MSC (2000):
Primary 11B50, 20D60
Posted:
April 1, 2003
MathSciNet review:
1974317
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Abstract:
By using Scherk's lemma we give a simple combinatorial proof of a theorem due to Bollobás and Leader. For any sequence of elements of an abelian group of order  , calling the sum of  terms of the sequence a  -sum, if 0 is not a  -sum, then there are at least   -sums.
References:
-
- 1.
- N. Alon and M. Dubiner, Zero-sum sets of prescribed size, in: ``Combinatorics, Paul Erdös is Eighty'', János Bolyai Math. Soc., 1993, pp.33-50. MR 94j:11016
- 2.
- B. Bollobás and I. Leader, The number of
 -sums modulo  , J. Number Theory 78 (1999), 27-35. MR 2000i:11036 - 3.
- P. Erdös, A. Ginzburg, and A. Ziv, Theorem in the additive number theory, Bull. Res. Council Israel(F) 10 (1961), 41-43.
- 4.
- H. Halberstam and K. F. Roth, ``Sequences'', Vol.I, Oxford Univ. Press, 1966. MR 35:1565
- 5.
- M. B. Nathanson, ``Additive Number Theory. Inverse Problems and the Geometry of Sumsets'', Volume 165 of Graduate Texts in Mathematics, Springer-Verlag, 1996. MR 98f:11011
- 6.
- P. Scherk, Solution to Problem 4466, Amer. Math. Monthly 62 (1955), 46-47.
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Additional Information:
Hong
Bing
Yu
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei 230026, Anhui, People's Republic of China
Email:
yuhb@ustc.edu.cn
DOI:
10.1090/S0002-9939-03-07091-6
PII:
S 0002-9939(03)07091-6
Received by editor(s):
December 5, 2001
Posted:
April 1, 2003
Additional Notes:
The author was supported by the National Natural Science Foundation of China
Communicated by:
David E. Rohrlich
Copyright of article:
Copyright
2003,
American Mathematical Society
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