T. Lulek

We demonstrate that the Robinson - Schensted - Knuth (RSK) algorithm admits a natural magnetic interpretation within the one-dimensional Heisenberg magnet, described within the famous Bethe Ansatz. Each magnetic configuration is just a word of length N, the number of nodes of the magnet, in the alphabet of n=2s+1 single-node spin projections. We point out that an n-tuply cover of the magnetic ring, with a separate copy for each letter of the alphabet of spins, provides a natural performance of the RSK algorithm and well motivates the procedure of standardization. Similarities and distinctions between various group-theoretic and combinatorial objects (configurations, words, Weyl and Young tableaux, wave packets etc.) have been discussed within the context of magnetic interpretation.