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

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

Published electronically:
September 29, 2003

MathSciNet review:
2053329

Full-text PDF

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.**T. Bohman, A sum packing problem of Erdos and the Conway-Guy sequence, Proc. Amer. Math. Soc., Vol. 124, No. 12, 3627-3636, 1996. MR**97b:11027****2.**P. Erdos, Problems and results in additive number theory, Colloque sur la Théorie des Nombres, Bruxelles, 1955, Liège; Masson and Cie, Paris, 1956. MR**18:18a****3.**J. H. Conway and R. K. Guy, Sets of natural numbers with distinct sums, Notices Amer. Math. Soc., Vol. 15, p. 345, 1968.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
11P99,
05D05

Retrieve articles in all journals with MSC (2000): 11P99, 05D05

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