In this note we generalize the definition of partial permutations of Ivanov and Kerov and we build a universal algebra which projects onto the m-centraliser algebra defined by Creedon. We use it to present a new proof for the polynomiality property of the structure coefficients of the m-centraliser algebra and to obtain upper bounds for the polynomial degrees.
A general framework for the polynomiality property of the structure coefficients of double-class algebras
Polynomialité des coefficients de structure des algèbres de doubles-classes
$k$-partial permutations and the center of the wreath product $\mathcal{S}_k\wr \mathcal{S}_n$ algebra
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