Abstract
We introduce two new concepts which are the $k$ to $k$ substitution and $k$ to $k$ exchange of a letter on infinite words. After studying the return words and the special factors of words obtaining by these applications on Sturmian words and modulo-recurrent words. Next, we establish the complexity functions of these words. Finally, we determine the palindromic complexity of these words.
Reference17 articles.
1. J. P. A LLOUCHE , Sur la complexité des suites infinies, Bull. Belg. Math. Soc. Simon Stevin, 1(1994), 133–
2. J. P. A LLOUCHE , M. B AAKE , J. C ASSAIGNE AND D. D AMANIK , Palindrome complexity, Theoret. Comput.
3. Sci., 292(2003), 9–33.
4. M. B ARRO , I. K ABOR ´ E , T. T APSOBA , About the words by k to k erasure of letter and the words of erased letters: Sturmian case, IJAM., 32(2)(2019), 189–204.
5. M. B ARRO , I. K ABOR ´ E , T. T APSOBA , On the words by k to k insertion of a letter in sturmian words, IJAM., 30(5)(2017), 387–400.