Mel NathansonAffiliation: Lehman College, CUNY Email: melvyn.nathanson@lehman.cuny.edu Title Of Talk: Sums of sets of lattice points Abstract: If $A$ is a nonempty subset of an additive abelian group $G$, then the $h$fold sumset is \[ hA = \{x_1 + \cdots + x_h : x_i \in A_i \text{ for } i=1,2,\ldots, h\}. \] We do not assume that $A$ contains the identity, nor that $A$ is symmetric, nor that $A$ is finite. The set $A$ is an $(r,\ell)$approximate group in $G$ if there exists a subset $X$ of $G$ such that $X \leq \ell$ and $rA \subseteq XA$. The set $A$ is an asymptotic $(r,\ell)$approximate group if the sumset $hA$ is an $(r,\ell)$approximate group for all sufficiently large $h$. It is proved that every polytope in a real vector space is an asymptotic $(r,\ell)$approximate group, that every finite set of lattice points is an asymptotic $(r,\ell)$approximate group, and that every finite subset of every abelian group is an asymptotic $(r,\ell)$approximate group. WARNING: This page contains MATHJAX
Last update made Sun Feb 21 07:30:07 PST 2016.
