## Representations of permutation groups |

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### Contents

An application to representation theory Symme | 62 |

An application to combinatorics The theory | 103 |

References | 167 |

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### Common terms and phrases

aik(f;n aik(f;TT algebraically closed apply basis group beads of colour Bruijn Burnside's lemma character table combinatorics complete system conjugacy classes conjugates contained corollary corresponding matrix Cyc(P cycle-index cyclic factor decomposition matrix defined diag dimension double cosets elements enumeration under group equal evaluate example f;TT finite group following holds G and H g e G group G Hence idempotent identity representation implies inertia group irreducible constituents K-representation Littlewood mapping Math matrix representation natural number necklace normal subgroup number of orbits number of types obtain orbits of G ordinary irreducible representations ordinary representation pairwise inequivalent permutation character permutation group permutation representation polynomial Proof rational integral Redfield representation F representation of G representation theory S-functions sentation splitting subgroup of index symmetric groups symmetrized inner products system of pairwise types of graphs underlying vector space values vector space Weyl groups wreath products yields