Question is edited Perhaps this formulation is clearer. It is well known that if a power of a primitive (i.e. not a proper power) word $u$ contains two different occurrences of a …

I'm currently working on subwords of cube-free binary words. A binary word is one composed of letters from a two-letter alphabet such as $\{0,1\}$. A word $y$ is a subword of $w$ …

Consider a totally ordered alphabet $A$ of $n$ letters. Let $W$ be the set of all words over $A$ which have no two letters equal. Then, for example, we can define the Knuth equival …

Let $w$ be a word in letters $x_1,...,x_n$. A value of $w$ is any word of the form $w(u_1,...,u_n)$ where $u_1,...,u_n$ are words. For example, $abaaba$ is a value of $x^2$. A word …

Recently, as part of some joint research, Tom Roby was led to a curious operation on strings of L's and R's which he calls "bounce-reading": We start by reading the string at the l …

I work now a lot with strings of characters and other finite sequences and found that I need many times a good notation for "cutting the end" a string. If $a$ is a finite sequence …

Let $u(x_1,...,x_n)$ be a word, $k\in \mathbb{N}$. We say that $u$ is $k$-avoidable if there exists an infinite word in $k$ letters $\{a_1,...,a_k\}$ which does not contain values …

I have encountered sets of the following type, consisting of words over a finite aphabet $A$. If $S$ is such a set, then $S$ is finite, No word in $S$ is part of another element …

A word $y$ is a subword of $w$ if there exist words $x$ and $z$ (possibly empty) such that $w=xyz$. Thus, $01$ is a subword of $0110$, but $00$ is not a subword of $0110$. I'm in …

I am looking for software which helps me do straightforward tasks in combinatorial algebra. Let me give an example of what I mean by a straightforward task: I have two graded (ge …