MathDB
Determine all superinvariant sets - ILL 1990 FIN2

Source:

September 18, 2010
algebratransformationTranslationinvariantIMO ShortlistIMO Longlist

Problem Statement

We call a set SS on the real line RR "superinvariant", if for any stretching AA of the set SS by the transformation taking xx to A(x)=x0+a(x−x0)A(x) = x_0 + a(x - x_0), where a>0a > 0, there exists a transformation B,B(x)=x+bB, B(x) = x + b, such that the images of SS under AA and BB agree; i.e., for any x∈Sx \in S, there is y∈Sy \in S such that A(x)=B(y)A(x) = B(y), and for any t∈St \in S, there is a u∈Su \in S such that B(t)=A(u).B(t) = A(u). Determine all superinvariant sets.
Back to ProblemsView on AoPS