On the structure coefficients of the centralizer algebra

In this paper, we generalize the definition of partial permutations of Ivanov and Kerov and we build a universal algebra which projects onto the [Formula: see text]-centralizer algebra defined by Creedon. We use it to present a new proof for the polynomiality property of the structure coefficients of the [Formula: see text]-centralizer algebra and to obtain upper bounds for the polynomial degrees.