Bethe ansatz and the geography of rigged strings

We demonstrate the way in which composition of two famous combinatorial bijections, of Robinson-Schensted and Kero,-Kirillov-Reshetikhin, applied to the Heisenberg model of magnetic ring with spin 1/2, defines the geography of rigged strings (which label exact eigenfunctions of the Bethe Ansatz) on the classical configuration space (the set of all positions of the system of r reversed spins). We point out that each I-string originates, in the language of this bijection, from an island of I consecutive reversed spins. We also explain travel of 1-strings along orbits of the translation group of the ring.