# Questions tagged [word-combinatorics]

Questions about combinatorics on languages of words, that is how many sequences of symbols with certain properties there are.

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### Hex Word Search Generator Algorithm

I want to create an algorithm to build a hex matrix with given: - max n rows - max m collumns - min t rown - min q collumns containing the specific words from a list: "example", "test", "algorithm"....
92 views

### Primitive word and cyclic rotations

Definition. A word $w \in \Sigma^*$ is primitive if $w=u^n \rightarrow n=1$. Is it true that a word is primitive if and only if its all cyclic rotations are dstinct?
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### What is language density used for?

If we have a langage $L$ over an alphabet $\Sigma$, then we can defined the density function of $L$ as : $$p_L(n) = | L \cap \Sigma^n |$$ I am wondering why it’s useful to study this function ...
293 views

### Word factorization in $O(n^2 \log n)$ time

Given two strings $S_1, S_2$, we write $S_1S_2$ for their concatenation. Given a string $S$ and integer $k\geq 1$, we write $(S)^k = SS\cdots S$ for the concatenation of $k$ copies of $S$. Now given a ...
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136 views

### Proving that $xy=yx$ iff $x^2y^2=z^2$

I was given the following problem as homework: Let $x$, $y$ be words over an alphabet $Σ$. Prove that $xy = yx$ iff there exists a word $z$ such that $x^2y^2 = z^2$. I was hinted that I am ...
381 views

### Ordered Cartesian Product

Say I have three sets: A = [banana, apple, grape] B = [1, 2, 3, 4] C = [Alice, Bob, Carol] I need to design an algorithm that gives me the Cartesian Product A ...
113 views

### Expressing the language of squares as a concatenation of two languages

Can the language $L = \{ vv : v \in \Sigma^* \}$ be expressed as the concatenation of two nontrivial languages? (A language is nontrivial if it differs from $\{\epsilon\}$.)
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### Given the alphabet $\{a, b, c\}$, how many words can we form with 4 letters?

Question: Given the alphabet $\{a, b, c\}$, how many words can we form with 4 letters? And how many words can we form with up to 4 letters? I was thinking about the logic behind this and came up with ...
91 views

### Given a permutation of n integers, how fast can a corresponding Standard Young's Tableau be created?

The Schensted insertion algorithm has an $O(n^2)$ running time, for constructing such a standard Young's Tableaux. But, since every permutation has a unique Young's tableau, there seems no reason as ...
62 views

### How many restricted length strings are there without significant repetitions

Let us fix an alphabet $\Sigma$ of size $c$, then we have the finite language $\Sigma^n$ which is the set of all $n$ length words. For each $N,M$ how many words are there in $\Sigma^n$ such that no ...
61 views