## Abstract

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 S_{k}≀ S_{n} algebra are polynomials in n with nonnegative integer coefficients. We use a universal algebra I∞k, which projects on the center Z(C[S_{k}≀ S_{n}]) for each n. We show that I∞k is isomorphic to the algebra of shifted symmetric functions on many alphabets.

Original language | English |
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Pages (from-to) | 389-412 |

Number of pages | 24 |

Journal | Journal of Algebraic Combinatorics |

Volume | 53 |

Issue number | 2 |

DOIs | |

Publication status | Published - Mar 2021 |

Externally published | Yes |

## Keywords

- Character theory
- k-partial permutations
- Shifted symmetric functions
- Structure coefficients
- Wreath product of symmetric groups

## ASJC Scopus subject areas

- Algebra and Number Theory
- Discrete Mathematics and Combinatorics

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