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Abstract

We demonstrate the way in which composition of two famous combinatorial bijections, of Robinson-Schensted and Kerov-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 $l$-string originates, in the language of this bijection, from an island of $l$ consecutive reversed spins. We also explain travel of $l$-strings along orbits of the translation group of the ring.