## Representations of Permutation Groups II |

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### Contents

Characters of wreath products | 3 |

An application to representation theory Symme trization of inner tensor products of represen | 62 |

An application to combinatorics The theory of enumeration under group action 10 | 103 |

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### Common terms and phrases

aik(f;n aik(f;TT algebraically closed application basis group beads of colour Bruijn Burnside's lemma c(tt character table combinatorics complete system conjugacy classes conjugates Cyc(P cycle-index decomposition matrix denotes double cosets Edited elements enumeration problems enumeration theorem equation evaluate f;TT finite group following holds G and H g e G G^Sn group action group G group reduction Hence idempotent identity representation inertia group irreducible constituents K-representation lemma Littlewood Math matrix representation natural number necklace normal subgroup number of orbits number of types obtain ordinary irreducible representations ordinary representation pairwise inequivalent permutation character permutation group permutation representation polynomial Proceedings 1974 Proof rational integral Redfield representation F representation of G representation theory respect S-functions selfassociated sentation splitting subgroup of index symmetric groups symmetrized inner products system of pairwise transitive types of graphs underlying vector space vector space Weyl groups wreath products yields