Dan Katz (Brown)
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A sumfree set is just what it probably sounds like; given an ambient
set with an addition rule, a subset A is sumfree if no two (not
necessarily distinct) elements of A sum to another element of A.
Sumfree sets of integers have been studied in some depth, but
little work has been done with respect to sumfree sets of vectors.
I will demonstrate new bounds on the maximum size of a sumfree set of vectors with bounded integer coefficients, and make a conjecture about the best possible result. I will also demonstrate a method of analysis that suggests the conjecture is correct, and talk about how this method may lead toward a full proof. |