What does it means "dissipative set" in the following context:
"If the set contains $3^n$ integer numbers, then it contains dissipative subset with $n$ elements"?
I have not found the definition related to the combinatoric...
What does it means "dissipative set" in the following context: "If the set contains $3^n$ integer numbers, then it contains dissipative subset with $n$ elements"? I have not found the definition related to the combinatoric... 


Maybe, you mean "a dissociated set"? A finite subset $A$ of an abelian group is called dissociated if all of its $2^{A}$ subset sums are pairwise distinct. It is certainly true that if $A$ is set of $3^n$ elements of an (arbitrary) abelian group, then $A$ contains an $n$element dissociated subset. Indeed, let $S$ be any maximal (by inclusion) dissociated subset of $A$. Then every element of $A$ can be written as a linear combination of the elements of $S$ with the coefficients in $\{1,0,1\}$. Consequently, $3^{S}\geA=3^n$, whence $S\ge n$. 

