Bases in some additive groups and the Erdo″s-Turán conjecture

Labib Haddad; C. Helou

doi:10.1016/j.jcta.2004.05.004

Bases in some additive groups and the Erdo″s-Turán conjecture

Labib Haddad, C. Helou

Penn State Brandywine

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8 Scopus citations

Abstract

We show that the analogue of the Erdos-Turán conjecture, for the number of representations by a basis of order two of an additive semi-group, does not hold in a variety of additive groups derived from those of certain fields. This is done by explicitly constructing some bases for which we estimate the maximal number of representations of the elements of the group as a sum of two elements from the given basis.

Original language	English (US)
Pages (from-to)	147-153
Number of pages	7
Journal	Journal of Combinatorial Theory. Series A
Volume	108
Issue number	1
DOIs	https://doi.org/10.1016/j.jcta.2004.05.004
State	Published - Oct 2004

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/j.jcta.2004.05.004

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abstract = "We show that the analogue of the Erdos-Tur{\'a}n conjecture, for the number of representations by a basis of order two of an additive semi-group, does not hold in a variety of additive groups derived from those of certain fields. This is done by explicitly constructing some bases for which we estimate the maximal number of representations of the elements of the group as a sum of two elements from the given basis.",

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Bases in some additive groups and the Erdo″s-Turán conjecture

Abstract

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