The combinatorics-on-words tag has no wiki summary.

**25**

votes

**1**answer

632 views

### “Nyldon words”: understanding a class of words factorizing the free monoid increasingly

BACKGROUND.
Let me first introduce some classical definitions, which appear, e.g., in §5 of Lothaire's Combinatorics on Words, in §5.1 of Reutenauer's Free Lie algebras, and in §6.1 of Victor ...

**16**

votes

**0**answers

386 views

### partition of infinite word onto permitted words

Consider words over binary alphabet $\{0,1\}$. Let $M$ be a set of finite words such that $M$ contains at least $c\cdot 2^n$ words of length $n$ for all large enough $n$ (for a constant $c$, ...

**16**

votes

**0**answers

432 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 of $u$ (i.e. words ...

**9**

votes

**0**answers

118 views

### Computing exact or asymptotics for number of strings over an alphabet of size $n$ that have no non-trivial substrings that appear more than once

I ran across a seemingly relatively simple combinatorics problem that appears open. For an alphabet of size $n$, let $A(n)$ be the number of strings over the alphabet that have no substring of length ...

**3**

votes

**0**answers

47 views

### Covariance matrix for number of powers in a word

A word over the alphabet $\{0,1\}$ of length $n$ may contain squares, cubes, and generally $k$th powers, where $2\le k\le n$. Let $O_k(w)$ denote the number of $k$th power occurrences in the word $w$.
...

**3**

votes

**0**answers

154 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 of $S$, and
every ...

**3**

votes

**0**answers

334 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 (generally ...

**2**

votes

**0**answers

86 views

### Counting strings with alternating letters with generating functions

It is a classical problem that of finding the generating function (GF) of the number of strings with length $n$ having $m$ different letters (basically, the problem reduces to that of writing the ...