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This is Algorithm A from Functional Programs for Generating Permutations (Topor, 1982). We have implemented Algorithm A in F# as follows. let rec put (a: ‘t) (p: List<‘t>) (q: List<‘t>) : List<‘t> = if p = q then a :: q else p.Head :: (put a p.Tail q) // a: an element // p: aRead more

It is required to generate only ONE palindromic permutation of given string s , if no palindrome is possible return -1 . NOTE : Do suggest other method to following one: By checking every other permutation to be palindromic or not, until we got one. Like code in python : import itertools def permutation(word): forRead more

For a partition $ \lambda \vdash n$ , the permutation representation $ M^{\lambda}$ of the symmetric group can be constructed in two ways. First, it may be written as the induced representation $ M^{\lambda} = 1\uparrow_{S_{\lambda}}^{S_n}$ . Second, it may be written as the $ S_n$ -module spanned by tabloids of shape $ \lambda$ ,Read more

Let $ A \in M_n$ . $ A$ is called reducible if $ A$ is permutation similar to a matrix of the form $ $ \begin{pmatrix} B & 0\ C &D \end{pmatrix} $ $ where $ B$ and $ D$ are square matrices. Reading a book I got stuck in the following lines: Obviously, $Read more

What is the number of terms of the unique multilinear polynomial $ f\in\Bbb F_2[x_{1,1},\dots,x_{n,n}]$ in $ n^2$ variables such that $ f$ vanishes only on matrices that are permutations? Are there good bounds? Note that such a polynomial should have $ S_n\times S_n$ symmetry. I think one can even guess how such a polynomial shouldRead more

Group Reduce means take an array can be translate to another one by a Cycles, then they’re the same. For example, orderless array {1,2,4} and {2,3,6} are the same by c1=Cycles[{{1,3,9,7},{2,6,8,4}}],because {1,2,4} -> {3,6,2} = {2,3,6}. Orderless array {1,2,4} and {2,3,6} are different by c2=Cycles[{{1,9},{2,8},{3,7},{4,6}}], but they’re the same by both c1 and c2. BackgroundRead more