Preface -- 1 The Misère Monoid of One-Handed Alternating Games -- 1.1 Introduction -- 1.1.1 Background -- 1.2 Equivalences -- 1.3 Outcomes -- 1.4 The Misère Monoid -- 2 Images of C-Sets and Related Large Sets under Nonhomogeneous Spectra -- 2.1 Introduction -- 2.2 The Various Notions of Size -- 2.3 The Functions fa and ha -- 2.4 Preservation of J -Sets, C-Sets, and C*-Sets -- 2.5 Preservation of Ideals -- 3 On the Differences Between Consecutive Prime Numbers, I -- 3.1 Introduction and Statement of Results -- 3.2 The Hardy-Littlewood Prime k-Tuple Conjectures -- 3.3 Inclusion-Exclusion for Consecutive Prime Numbers -- 3.4 Proof of the Theorem -- 4 On Sets of Integers Which Are Both Sum-Free and Product-Free -- 4.1 Introduction -- 4.2 The Upper Density -- 4.3 An Upper Bound for the Density in ℤ/nℤ -- 4.4 Examples With Large Density -- 5 Four Perspectives on Secondary Terms in the Davenport-Heilbronn Theorems -- 5.1 Introduction -- 5.2 Counting Fields in General -- 5.2.1 Counting Torsion Elements in Class Groups -- 5.3 Davenport-Heilbronn, Delone-Faddeev, and the Main Terms -- 5.3.1 TheWork of Belabas, Bhargava, and Pomerance -- 5.4 The Four Approaches -- 5.5 The Shintani Zeta-Function Approach -- 5.5.1 Nonequidistribution in Arithmetic Progressions -- 5.6 A Refined Geometric Approach -- 5.6.1 Origin of the Secondary Term -- 5.6.2 A Correspondence for Cubic Forms -- 5.7 Equidistribution of Heegner Points -- 5.7.1 Heegner Points and Equidistribution -- 5.8 Hirzebruch Surfaces and the Maroni Invariant -- 5.9 Conclusion -- 6 Spotted Tilings and n-Color Compositions -- 6.1 Background -- 6.2 n-Color Composition Enumerations -- 6.3 Conjugable n-Color Compositions -- 7 A Class ofWythoff-Like Games -- 7.1 Introduction -- 7.2 Constant Function -- 7.2.1 A Numeration System.

7.2.2 Strategy Tractability and Structure of the P-Positions -- 7.3 Superadditive Functions -- 7.4 Polynomial -- 7.5 Further Work -- 8 On the Multiplicative Order of FnC1=Fn Modulo Fm -- 8.1 Introduction -- 8.2 Preliminary Results -- 8.3 Proof of Theorem 8.1 -- 8.4 Comments and Numerical Results -- 9 Outcomes of Partizan Euclid -- 9.1 Introduction -- 9.2 Game Tree Structure -- 9.3 Reducing the Signature -- 9.3.1 Algorithm -- 9.4 Outcome Observations -- 9.5 Open Questions -- 10 Lecture Hall Partitions and theWreath Products Ck ≀ Sn -- 10.1 Introduction -- 10.2 Lecture Hall Partitions -- 10.3 Statistics on Ck ≀ Sn -- 10.4 Statistics on s-Inversion Sequences -- 10.5 From Statistics on Ck o Sn to Statistics on In,k -- 10.6 Lecture Hall Polytopes and s-Inversion Sequences -- 10.7 Lecture Hall Partitions and the Inversion Sequences In,k -- 10.8 A Lecture Hall Statistic on Ck ≀ Sn -- 10.9 Inflated Eulerian Polynomials for Ck ≀ Sn -- 10.10 Concluding Remarks.