A simple proof of a theorem of Bollobás and Leader
Author:
Hong Bing Yu
Journal:
Proc. Amer. Math. Soc. 131 (2003), 26392640
MSC (2000):
Primary 11B50, 20D60
Published electronically:
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.
 1.
N. Alon and M. Dubiner, Zerosum sets of prescribed size, in: ``Combinatorics, Paul Erdös is Eighty'', János Bolyai Math. Soc., 1993, pp.3350. MR 94j:11016
 2.
B. Bollobás and I. Leader, The number of sums modulo , J. Number Theory 78 (1999), 2735. MR 2000i:11036
 3.
P. Erdös, A. Ginzburg, and A. Ziv, Theorem in the additive number theory, Bull. Res. Council Israel(F) 10 (1961), 4143.
 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, SpringerVerlag, 1996. MR 98f:11011
 6.
P. Scherk, Solution to Problem 4466, Amer. Math. Monthly 62 (1955), 4647.
 1.
 N. Alon and M. Dubiner, Zerosum sets of prescribed size, in: ``Combinatorics, Paul Erdös is Eighty'', János Bolyai Math. Soc., 1993, pp.3350. MR 94j:11016
 2.
 B. Bollobás and I. Leader, The number of sums modulo , J. Number Theory 78 (1999), 2735. MR 2000i:11036
 3.
 P. Erdös, A. Ginzburg, and A. Ziv, Theorem in the additive number theory, Bull. Res. Council Israel(F) 10 (1961), 4143.
 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, SpringerVerlag, 1996. MR 98f:11011
 6.
 P. Scherk, Solution to Problem 4466, Amer. Math. Monthly 62 (1955), 4647.
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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:
http://dx.doi.org/10.1090/S0002993903070916
PII:
S 00029939(03)070916
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
