Approximations of additive squares in infinite words

Details Approximations of additive squares in infinite words Approximations of additive squares in infinite words

2011-08-03

arxiv.org/abs/1108.0739v1

Mathematics

Combinatorics

Scientific paper

We show that every infinite word $\omega$ on a finite subset of $\mathbb{Z}$
must contain arbitrarily large factors $B_1B_2$ which are "close" to being
\textit{additive squares}. We also show that for all $k>1, \ \omega$ must
contain a factor $U_1U_2 ... U_k$ where $U_1,U_2,..., U_k$ all have the same
\textit{average.}

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