Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $k$-partial permutations and the center of the wreath product
  $\mathcal{S}_k\wr \mathcal{S}_n$ algebra   We generalize the concept of partial permutations of Ivanov and Kerov and
introduce $k$-partial permutations. This allows us to show that the structure
coefficients of the center of the wreath product $\mathcal{S}_k\wr
\mathcal{S}_n$ algebra are polynomials in $n$ with non-negative integer
coefficients. We use a universal algebra $\mathcal{I}_\infty^k$ which projects
on the center $Z(\mathbb{C}[\mathcal{S}_k\wr \mathcal{S}_n])$ for each $n.$ We
show that $\mathcal{I}_\infty^k$ is isomorphic to the algebra of shifted
symmetric functions on many alphabets.

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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio