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We study the classical complexity of k to k insertion words of a letter in Sturmian words. Then, we determine the Abelian complexity and palindromic complexity of these words. Finally, we show that the k to k insertion of a letter x in Sturmian words preserves the palindromic richness of Sturmian words if and only if k = 1. AMS Subject Classification: 68R15, 11B85

ON THE WORDS BY $k$ TO $k$ INSERTION OF A LETTER IN STURMIAN WORDS