Abelian complexity of infinite words

Karel Břinda, Edita Pelantová, Ondřej Turek
2018 Zenodo  
This thesis deals with Abelian complexity of infinite words, i.e., function describing complexity of a given infinite word using sets of Parikh vectors of finite factors of the word. Some of already known results for words generated by primitive substitutions (including connection between Abelian complexity, balance function, discrepancy function and matrix of a primitive substitution) are summarized. Then an explicit formula for Abelian complexity of infinite words associated with quadratic
more » ... ry numbers is derived. In addition, a new toolkit TigrWords, which facilitates study of infinite words approximated by their prefixes and may serve to discover of new hypotheses, is described.
doi:10.5281/zenodo.2112128 fatcat:j4gxptknm5dkbg5d65ccjnvmfu