User greg - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T11:36:15Z http://mathoverflow.net/feeds/user/30105 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/116833/unique-sums-in-a-finite-direct-product-of-sets-of-integers unique sums in a finite direct product of sets of integers Greg 2012-12-20T01:48:01Z 2012-12-20T11:11:21Z <p>I am an algebraist, and I am wondering if there is a definition for the following:</p> <p>Let $A_1$, $A_2$, $\ldots, A_n$ be sets of integers (or more generally, subsets of a group $G$). Say that (for the purposes of this question) $A_1\times A_2\cdots\times A_n$ is <em>special</em> provided that whenever $a_1+a_2+\cdots+a_n=b_1+b_2\cdots+b_n$ with each $a_i,b_i\in A_i$, $1\leq i\leq n$, then $a_i=b_i$ for all $i$, $1\leq i\leq n$. </p> <p>Is there some terminology for this property? Any information would be appreciated.</p>