Geodesic
Sets with few differences in abelian groups
Mitchell Lee1
1Harvard University
The electronic journal of combinatorics, Tome 25 (2018) no. 3
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Let $(G, +)$ be an abelian group. In 2004, Eliahou and Kervaire found an explicit formula for the smallest possible cardinality of the sumset $A+A$, where $A \subseteq G$ has fixed cardinality $r$. We consider instead the smallest possible cardinality of the difference set $A-A$, which is always greater than or equal to the smallest possible cardinality of $A+A$ and can be strictly greater. We conjecture a formula for this quantity and prove the conjecture in the case that $G$ is an elementary abelian $p$-group. This resolves a conjecture of Bajnok and Matzke on signed sumsets.
DOI : 10.37236/5502
Classification : 11B13, 11B75, 05D99, 20K01
Mots-clés : abelian groups, sumsets, Cauchy-Davenport theorem

Mitchell Lee  1

1 Harvard University 
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Mitchell Lee. Sets with few differences in abelian groups. The electronic journal of combinatorics, Tome 25 (2018) no. 3. doi: 10.37236/5502

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