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The study of the structure of infinite words having bounded abelian complexity was initiated by G. Richomme, K. Saari, and L. Q. Zamboni. In this note we define bounded additive complexity for infinite words over a finite subset of Z^m. We provide an alternative proof of one of the results of Richomme, Saari, and Zamboni.
A universal word for a finite alphabet $A$ and some integer $ngeq 1$ is a word over $A$ such that every word in $A^n$ appears exactly once as a subword (cyclically or linearly). It is well-known and easy to prove that universal words exist for any $A
Stankova and West showed that for any non-negative integer $s$ and any permutation $gamma$ of ${4,5,dots,s+3}$ there are as many permutations that avoid $231gamma$ as there are that avoid $312gamma$. We extend this result to the setting of words.
We present results on the existence of long arithmetic progressions in the Thue-Morse word and in a class of generalised Thue-Morse words. Our arguments are inspired by van der Waerdens proof for the existence of arbitrary long monochromatic arithmet
Let S be a double occurrence word, and let M_S be the words interlacement matrix, regarded as a matrix over GF(2). Gauss addressed the question of which double occurrence words are realizable by generic closed curves in the plane. We reformulate answ
In this paper, we investigate statistics on alternating words under correspondence between ``possible reflection paths within several layers of glass and ``alternating words. For $v=(v_1,v_2,cdots,v_n)inmathbb{Z}^{n}$, we say $P$ is a path within $n$