Tagged Questions

1answer
181 views

A property of periodic words

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 …
4answers
384 views

Subwords of cube-free binary words

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 $w$ …
1answer
387 views

Analogues of the Knuth and Forgotten equivalences on permutations: have they been studied?

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 …
2answers
519 views

Ubiquitous Zimin words

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 …
3answers
648 views

an operation on binary strings

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 …
1answer
277 views

Notation for ends of a string

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 …
0answers
286 views

Avoidable words

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 …
0answers
134 views

Generalised de Bruijn Graph

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 …
3answers
1k views

Cube-free infinite binary words

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 …
0answers
254 views

Software for Combinatorial Algebra sought

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 …
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