Chapter Ⅰ THE CALCUIUS OF PERMUTATIONS § 1 Permutations § 2 The Symmetric Group fn § 3 Cycles and Transpositions § 4 Odd and Even Permutations § 5 Classes of Permutations § 7 The Positive and Negative Symmetric Groups on r Letters Chapter Ⅱ THE CALCULUS OF TABIEAUX § 1 Shapes and Tableaux § 2 The Substitutional Expressions P and N § 3 The Product PrNs § 4 The Expressions E § 5 von Neumann's Theorem § 6 Young's Formula § 7 Tableaux of Different Shapes Chapter Ⅲ THE SEMI-NORMAL REPRESENTATION § 1 Standard Tableaux § 2 The Evaluation of fa § 3 The Semi-normal Units e § 4 Certain Fundamental Formulae § 5 The Irreducible Semi-normal Representations of fn § 6 Expressions which do not Involve the Last Letter § 7 The Semi-normal Matrix for E § 8 The Matrices U § 9 The Matrices U Chapter Ⅳ THE ORTHOGONAL AND NATURAL REPRESENTATIONS § 1 Equivalent Representations § 2 The Invariant Quadratic § 3 The Tableau Function § 4 The Orthogonal Representation § 5 The Matrix § 6 The Natural Representation § 7 Expressions for the Units g § 8 Equivalence of the Natural and Semi-normal Representations Chapter Ⅴ GROUP CHARACTERS § 1 The Expressions Cα § 2 The Expressions Tα § 3 The Relations between the Expressions Tκ and Cκ § 4 The Group Characters of fn § 5 The Evaluation of the Group Characters § 6 Reduction Formulae § 7 Littlewood's Theorem Chapter Ⅵ SUBSTITUTIONAL EQUATIONS § 1 Minimum Functions § 2 The Master Idempotent § 3 The Substitutional Properties of Functions § 4 The Number of Independent Solutions of LX = 0 § 5 The Solution of the Equation LX = 0 § 6 Functions which are Invariant under a Group of Substitutional Expressions § 7 Some Special Cases § 8 The Equation LX = R Appendix TABLES FOR THE CASE n = 3 Bibliography Index
