Rearranging series of vectors on a small set.

We consider a variation of the Lévy–Steinitz theorem where one rearranges only a small number of terms. In particular, we study the set of obtainable rearrangements of a multidimensional series by a permutation σ : ω → ω such that { n ∈ ω : σ ( n ) ≠ n } ∈ I for some proper ideal I ⊂ P ( ω ) . [ABSTRACT FROM AUTHOR]