Small asymmetric sumsets in elementary abelian 2-groups
Abstract
Let A and B be subsets of an elementary abelian 2-group G, none of which are contained in a coset of a proper subgroup. Extending onto potentially distinct summands a result of Hennecart and Plagne, we show that if |A+B|<|A|+|B|, then either A+B=G, or the complement of A+B in G is contained in a coset of a subgroup of index at least 8, whence |A+B| is at least 7/8 |G|. We indicate conditions for the containment to be strict, and establish a refinement in the case where the sizes of A and B differ significantly.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2011
- DOI:
- 10.48550/arXiv.1109.4670
- arXiv:
- arXiv:1109.4670
- Bibcode:
- 2011arXiv1109.4670E
- Keywords:
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- Mathematics - Combinatorics
- E-Print:
- 6 pages