| Preface | 5 |
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| 1 The Misère Monoid of One-Handed Alternating Games | 11 |
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| 1.1 Introduction | 11 |
| 1.1.1 Background | 12 |
| 1.2 Equivalences | 14 |
| 1.3 Outcomes | 20 |
| 1.4 The Misère Monoid | 22 |
| 2 Images of C-Sets and Related Large Sets under Nonhomogeneous Spectra | 25 |
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| 2.1 Introduction | 25 |
| 2.2 The Various Notions of Size | 29 |
| 2.3 The Functions fa and ha | 35 |
| 2.4 Preservation of J -Sets, C-Sets, and C*-Sets | 37 |
| 2.5 Preservation of Ideals | 43 |
| 3 On the Differences Between Consecutive Prime Numbers, I | 47 |
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| 3.1 Introduction and Statement of Results | 47 |
| 3.2 The Hardy–Littlewood Prime k-Tuple Conjectures | 48 |
| 3.3 Inclusion–Exclusion for Consecutive Prime Numbers | 49 |
| 3.4 Proof of the Theorem | 52 |
| 4 On Sets of Integers Which Are Both Sum-Free and Product-Free | 55 |
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| 4.1 Introduction | 55 |
| 4.2 The Upper Density | 57 |
| 4.3 An Upper Bound for the Density in Z/nZ | 60 |
| 4.4 Examples With Large Density | 61 |
| 5 Four Perspectives on Secondary Terms in the Davenport–Heilbronn Theorems | 65 |
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| 5.1 Introduction | 65 |
| 5.2 Counting Fields in General | 66 |
| 5.2.1 Counting Torsion Elements in Class Groups | 69 |
| 5.3 Davenport–Heilbronn, Delone–Faddeev, and the Main Terms | 70 |
| 5.3.1 TheWork of Belabas, Bhargava, and Pomerance | 71 |
| 5.4 The Four Approaches | 72 |
| 5.5 The Shintani Zeta-Function Approach | 73 |
| 5.5.1 Nonequidistribution in Arithmetic Progressions | 76 |
| 5.6 A Refined Geometric Approach | 77 |
| 5.6.1 Origin of the Secondary Term | 78 |
| 5.6.2 A Correspondence for Cubic Forms | 79 |
| 5.7 Equidistribution of Heegner Points | 80 |
| 5.7.1 Heegner Points and Equidistribution | 81 |
| 5.8 Hirzebruch Surfaces and the Maroni Invariant | 83 |
| 5.9 Conclusion | 84 |
| 6 Spotted Tilings and n-Color Compositions | 89 |
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| 6.1 Background | 89 |
| 6.2 n-Color Composition Enumerations | 91 |
| 6.3 Conjugable n-Color Compositions | 96 |
| 7 A Class ofWythoff-Like Games | 101 |
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| 7.1 Introduction | 101 |
| 7.2 Constant Function | 103 |
| 7.2.1 A Numeration System | 104 |
| 7.2.2 Strategy Tractability and Structure of the P-Positions | 108 |
| 7.3 Superadditive Functions | 109 |
| 7.4 Polynomial | 113 |
| 7.5 Further Work | 116 |
| 8 On the Multiplicative Order of FnC1=Fn Modulo Fm | 119 |
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| 8.1 Introduction | 119 |
| 8.2 Preliminary Results | 120 |
| 8.3 Proof of Theorem 8.1 | 124 |
| 8.4 Comments and Numerical Results | 130 |
| 9 Outcomes of Partizan Euclid | 133 |
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| 9.1 Introduction | 133 |
| 9.2 Game Tree Structure | 135 |
| 9.3 Reducing the Signature | 138 |
| 9.3.1 Algorithm | 142 |
| 9.4 Outcome Observations | 143 |
| 9.5 Open Questions | 144 |
| 10 Lecture Hall Partitions and theWreath Products Ck . Sn | 147 |
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| 10.1 Introduction | 147 |
| 10.2 Lecture Hall Partitions | 148 |
| 10.3 Statistics on Ck . Sn | 149 |
| 10.4 Statistics on s-Inversion Sequences | 150 |
| 10.5 From Statistics on Ck o Sn to Statistics on In,k | 151 |
| 10.6 Lecture Hall Polytopes and s-Inversion Sequences | 153 |
| 10.7 Lecture Hall Partitions and the Inversion Sequences In,k | 155 |
| 10.8 A Lecture Hall Statistic on Ck . Sn | 158 |
| 10.9 Inflated Eulerian Polynomials for Ck . Sn | 160 |
| 10.10 Concluding Remarks | 163 |
