Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-27T07:58:21.243Z Has data issue: false hasContentIssue false
  • English
  • Français

Comments on Y. O. Hamidoune's Paper ‘Adding Distinct Congruence Classes’

Published online by Cambridge University Press:  09 March 2016

BÉLA BAJNOK
BÉLA BAJNOK*
Affiliation:
Department of Mathematics, Gettysburg College, Gettysburg, PA 17325-1486, USA (e-mail: bbajnok@gettysburg.edu)
Get access Rights & Permissions [Opens in a new window]

Abstract

The main result in Y. O. Hamidoune's paper ‘Adding distinct congruence classes' (Combin. Probab. Comput.7 (1998) 81–87) is as follows. If S is a generating subset of a cyclic group G such that 0 ∉ S and |S| ⩾ 5, then the number of sums of the subsets of S is at least min(|G|, 2|S|). Unfortunately, the argument of the author, who, sadly, passed away in 2011, relies on a lemma whose proof is incorrect; in fact, the lemma is false for all cyclic groups of even order. In this short note we point out this mistake, correct the proof, and discuss why the main result is actually true for all finite abelian groups.

Keywords

Primary 11B75Secondary 05D9911B2511P7020K01
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 25 , Issue 5 , September 2016 , pp. 641 - 644
Copyright
Copyright © Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Diderrich, G. T. and Mann, H. B. (1973) Combinatorial problems in finite abelian groups. In A Survey of Combinatorial Theory (Srivastava, J. N. et al., eds), North-Holland, pp. 95–100.CrossRefGoogle Scholar
[2] Gallardo, L., Grekos, G., Habsieger, L., Hennecart, F., Landreau, B. and Plagne, A. (2002) Restricted addition in $\mathbb{Z}/n\mathbb{Z}$ and an application to the Erdős–Ginzburg–Ziv problem. J. London Math. Soc. (2) 65 513–523.Google Scholar
[3] Hamidoune, Y. O. (1998) Adding distinct congruence classes. Combin. Probab. Comput. 7 81–87.CrossRefGoogle Scholar