Effective Khovanskii, Ehrhart Polytopes, and the Erdős Multiplication Table Problem

Anna Margarethe Limbach, Robert Scheidweiler, Eberhard Triesch

Let $P(k,n)$ be the set of products of $k$ factors from the set $\{1,\dots ,n\}.$ In 1955, Erdős posed the problem of determining the order of magnitude of $|P(2,n)|$ and prov…