Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shuffling matrices, Kronecker product and Discrete Fourier Transform   We define and investigate a family of permutations matrices, called shuffling
matrices, acting on a set of $N=n_1\cdots n_m$ elements, where $m\geq 2$ and
$n_i\geq 2$ for any $i=1,\ldots, m$. These elements are identified with the
vertices of the $m$-th level of a rooted tree with branch indices $(n_1,\ldots,
n_m)$. Each of such matrices is induced by a permutation of $Sym(m)$ and it
turns out that, in the case in which one considers the cyclic permutation $(1\
\ldots\ m)$, the corresponding permutation is the classical perfect shuffle. We
give a combinatorial interpretation of these permutations in terms of
lexicographic order of the vertices of the tree. This allows us to describe
their fixed points. We show that our permutation matrices can be used to let
the Kronecker product of matrices commute or, more generally, rearrange in an
arbitrary order. Moreover, we show that the group generated by such
permutations does depend only on the branch indices of the tree, but it is
independent from their order. In the case in which such indices coincide, we
prove that the corresponding group is a copy of $Sym(m)$ inside $Sym(n^m)$.
Finally, we give an application of shuffling matrices in the context of the
Discrete Fourier Transform.

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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: ao-sci