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 nonnegative 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.

我们概括了Ivanov和Kerov的部分置换的概念，并介绍了k-部分置换。这使我们能够证明，花圈乘积\（{\ mathcal {S}} _ k \ wr {\ mathcal {S}} _ n \）代数的结构系数是n中具有非负整数系数的多项式。我们使用通用代数\（{\ mathcal {I}} _ \ infty ^ k \），它投影在中心\（Z（{\ mathbb {C}} [{\ mathcal {S}} _ k \ wr { \ mathcal {S}} _ n]）\）每个n。我们证明\（{\ mathcal {I}} _ \ infty ^ k \）与许多字母上的对称函数移位的代数同构。