# Questions tagged [permutations]

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### Are permutations of context-free languages context-free?

Given a context-free language $L$, define the language $p(L)$ as containing all permutations of strings in $L$ (i.e. all strings in $L$ such that the order of symbols is not important). Is $p(L)$ ...
670 views

### Polynomial time solution for bipartite matching

Inspired by this StackOverflow question, I am wondering if there is an efficient algorithm for the following problem: Assume $n$ items and $n$ boxes, with all boxes numbered numerically and all ...
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### Indexing a random permutation

I am curious if there exists a method for specifying a permutation $F_k: X \to X$ with a small(ish) $k$. Something that comes very close to my goal is a block cipher, say AES. But block ciphers have ...
328 views

### Random permutations by probability matrix

I have the following problem: I need to generate $\ell$ random permutations each of length $n$ from a list of $m$ elements ($m \ge n$) by a predefined probability matrix $P$ of size $n$ x $m$. ...
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### Counting permutations whose elements are not exactly their index ± 1

This is a special case of the question: Counting permutations whose elements are not exactly their index ± M The $M=0$ case has already been solved, but no one was sure how to work out the non-...
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### Algorithm to generate integer sets fulfills restrictions

I'm trying to solve the following problem. Input positive integers $v$, $b$ and $\ell$. ($\ell\leq v\leq b\ell$.) Output A list $S_1, \dots, S_k$ of all possible integer multisets (a ...
Is there any efficient algorithm which is able to generate nearly uniform samples of permutations in case of position restrictions? Consider $N \times N$ restriction matrices $R$, that is matrices ...