Recognizing Sumsets is NP-Complete
Sumsets are central objects in additive combinatorics. In 2007, Granville asked whether one
can efficiently recognize whether a given set S is a sumset, ie whether there is a set A such …
can efficiently recognize whether a given set S is a sumset, ie whether there is a set A such …
Sumsets in the Hypercube
A subset $ S $ of the Boolean hypercube $\mathbb {F} _2^ n $ is a sumset if $ S= A+ A=\{a+
b\|\a, b\in A\} $ for some $ A\subseteq\mathbb {F} _2^ n $. We prove that the number of …
b\|\a, b\in A\} $ for some $ A\subseteq\mathbb {F} _2^ n $. We prove that the number of …