A vector-sum theorem in two-dimensional space
In the spirit of a classical reordering theorem by Steinitz, the authors construct a number \(C\leq 18\) such that every finite set \(X\subset [- 1,1]\times [-1,1]\) with sum zero can be ordered such that the sum of the first k elements belongs to the rectangle [-1,1]\(\times [-C,C]\), for every k. The proof gives an O((card X)\({}^ 2)\) algorithm to obtain such an ordering of X.
scientific article; zbMATH DE number 3927800
scientific article