On Bohman's conjecture related to a sum packing problem of Erdos

Authors:
R. Ahlswede, H. Aydinian and L. H. Khachatrian

Journal:
Proc. Amer. Math. Soc. **132** (2004), 1257-1265

MSC (2000):
Primary 11P99; Secondary 05D05

Published electronically:
September 29, 2003

MathSciNet review:
2053329

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Abstract | References | Similar Articles | Additional Information

Abstract: Motivated by a sum packing problem of Erdos, Bohman discussed an extremal geometric problem which seems to have an independent interest. Let be a hyperplane in such that . The problem is to determine

Bohman (1996) conjectured that

We show that for some constants we have --disproving the conjecture. We also consider a more general question of the estimation of , when , .

**1.**Tom Bohman,*A sum packing problem of Erdős and the Conway-Guy sequence*, Proc. Amer. Math. Soc.**124**(1996), no. 12, 3627–3636. MR**1363448**, 10.1090/S0002-9939-96-03653-2**2.**P. Erdös,*Problems and results in additive number theory*, Colloque sur la Théorie des Nombres, Bruxelles, 1955, George Thone, Liège; Masson and Cie, Paris, 1956, pp. 127–137. MR**0079027****3.**J. H. Conway and R. K. Guy, Sets of natural numbers with distinct sums, Notices Amer. Math. Soc., Vol. 15, p. 345, 1968.

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Additional Information

**R. Ahlswede**

Affiliation:
Department of Mathematics, University of Bielefeld, POB 100131, 33501 Bielefeld, Germany

Email:
ahlswede@mathematik.uni-bielefeld.de

**H. Aydinian**

Affiliation:
Department of Mathematics, University of Bielefeld, POB 100131, 33501 Bielefeld, Germany

Email:
ayd@mathematik.uni-bielefeld.de

**L. H. Khachatrian**

Affiliation:
Department of Mathematics, University of Bielefeld, POB 100131, 33501 Bielefeld, Germany

Email:
lk@mathematik.uni-bielefeld.de

DOI:
https://doi.org/10.1090/S0002-9939-03-07188-0

Received by editor(s):
October 22, 2001

Received by editor(s) in revised form:
August 22, 2002, and January 15, 2003

Published electronically:
September 29, 2003

Communicated by:
John R. Stembridge

Article copyright:
© Copyright 2003
American Mathematical Society