A simple proof of a theorem of Bollobás and Leader

Author:
Hong Bing Yu

Journal:
Proc. Amer. Math. Soc. **131** (2003), 2639-2640

MSC (2000):
Primary 11B50, 20D60

DOI:
https://doi.org/10.1090/S0002-9939-03-07091-6

Published electronically:
April 1, 2003

MathSciNet review:
1974317

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Abstract | References | Similar Articles | Additional Information

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.

**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:
https://doi.org/10.1090/S0002-9939-03-07091-6

Received by editor(s):
December 5, 2001

Published electronically:
April 1, 2003

Additional Notes:
The author was supported by the National Natural Science Foundation of China

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 2003
American Mathematical Society