The abelian complexity of infinite words and the Frobenius problem
Combinatorics
2019-07-22 v1
Abstract
We study the following problem, first introduced by Dekking. Consider an infinite word x over an alphabet {0,1,...,k-1} and a semigroup homomorphism S:{0,1,...,k-1}* -> N. Let L_x denote the set of factors of x. What conditions on S and the abelian complexity of x guarantee that S(L_x) contains all but finitely many elements of N? We examine this question for some specific infinite words x having different abelian complexity functions.
Cite
@article{arxiv.1907.08247,
title = {The abelian complexity of infinite words and the Frobenius problem},
author = {Ian Kaye and Narad Rampersad},
journal= {arXiv preprint arXiv:1907.08247},
year = {2019}
}
Comments
18 pages