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

  • BÉLA BAJNOK (a1)

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.

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[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. 95100.
[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 513523.
[3] Hamidoune, Y. O. (1998) Adding distinct congruence classes. Combin. Probab. Comput. 7 8187.

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

  • BÉLA BAJNOK (a1)

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