Combinatorial Number Theory

1 - Preface [Seite 5]
2 - 1 The Misère Monoid of One-Handed Alternating Games [Seite 11]
2.1 - 1.1 Introduction [Seite 11]
2.1.1 - 1.1.1 Background [Seite 12]
2.2 - 1.2 Equivalences [Seite 14]
2.3 - 1.3 Outcomes [Seite 20]
2.4 - 1.4 The Misère Monoid [Seite 22]
3 - 2 Images of C-Sets and Related Large Sets under Nonhomogeneous Spectra [Seite 25]
3.1 - 2.1 Introduction [Seite 25]
3.2 - 2.2 The Various Notions of Size [Seite 29]
3.3 - 2.3 The Functions fa and ha [Seite 35]
3.4 - 2.4 Preservation of J -Sets, C-Sets, and C*-Sets [Seite 37]
3.5 - 2.5 Preservation of Ideals [Seite 43]
4 - 3 On the Differences Between Consecutive Prime Numbers, I [Seite 47]
4.1 - 3.1 Introduction and Statement of Results [Seite 47]
4.2 - 3.2 The Hardy-Littlewood Prime k-Tuple Conjectures [Seite 48]
4.3 - 3.3 Inclusion-Exclusion for Consecutive Prime Numbers [Seite 49]
4.4 - 3.4 Proof of the Theorem [Seite 52]
5 - 4 On Sets of Integers Which Are Both Sum-Free and Product-Free [Seite 55]
5.1 - 4.1 Introduction [Seite 55]
5.2 - 4.2 The Upper Density [Seite 57]
5.3 - 4.3 An Upper Bound for the Density in Z/nZ [Seite 60]
5.4 - 4.4 Examples With Large Density [Seite 61]
6 - 5 Four Perspectives on Secondary Terms in the Davenport-Heilbronn Theorems [Seite 65]
6.1 - 5.1 Introduction [Seite 65]
6.2 - 5.2 Counting Fields in General [Seite 66]
6.2.1 - 5.2.1 Counting Torsion Elements in Class Groups [Seite 69]
6.3 - 5.3 Davenport-Heilbronn, Delone-Faddeev, and the Main Terms [Seite 70]
6.3.1 - 5.3.1 TheWork of Belabas, Bhargava, and Pomerance [Seite 71]
6.4 - 5.4 The Four Approaches [Seite 72]
6.5 - 5.5 The Shintani Zeta-Function Approach [Seite 73]
6.5.1 - 5.5.1 Nonequidistribution in Arithmetic Progressions [Seite 76]
6.6 - 5.6 A Refined Geometric Approach [Seite 77]
6.6.1 - 5.6.1 Origin of the Secondary Term [Seite 78]
6.6.2 - 5.6.2 A Correspondence for Cubic Forms [Seite 79]
6.7 - 5.7 Equidistribution of Heegner Points [Seite 80]
6.7.1 - 5.7.1 Heegner Points and Equidistribution [Seite 81]
6.8 - 5.8 Hirzebruch Surfaces and the Maroni Invariant [Seite 83]
6.9 - 5.9 Conclusion [Seite 84]
7 - 6 Spotted Tilings and n-Color Compositions [Seite 89]
7.1 - 6.1 Background [Seite 89]
7.2 - 6.2 n-Color Composition Enumerations [Seite 91]
7.3 - 6.3 Conjugable n-Color Compositions [Seite 96]
8 - 7 A Class ofWythoff-Like Games [Seite 101]
8.1 - 7.1 Introduction [Seite 101]
8.2 - 7.2 Constant Function [Seite 103]
8.2.1 - 7.2.1 A Numeration System [Seite 104]
8.2.2 - 7.2.2 Strategy Tractability and Structure of the P-Positions [Seite 108]
8.3 - 7.3 Superadditive Functions [Seite 109]
8.4 - 7.4 Polynomial [Seite 113]
8.5 - 7.5 Further Work [Seite 116]
9 - 8 On the Multiplicative Order of FnC1=Fn Modulo Fm [Seite 119]
9.1 - 8.1 Introduction [Seite 119]
9.2 - 8.2 Preliminary Results [Seite 120]
9.3 - 8.3 Proof of Theorem 8.1 [Seite 124]
9.4 - 8.4 Comments and Numerical Results [Seite 130]
10 - 9 Outcomes of Partizan Euclid [Seite 133]
10.1 - 9.1 Introduction [Seite 133]
10.2 - 9.2 Game Tree Structure [Seite 135]
10.3 - 9.3 Reducing the Signature [Seite 138]
10.3.1 - 9.3.1 Algorithm [Seite 142]
10.4 - 9.4 Outcome Observations [Seite 143]
10.5 - 9.5 Open Questions [Seite 144]
11 - 10 Lecture Hall Partitions and theWreath Products Ck . Sn [Seite 147]
11.1 - 10.1 Introduction [Seite 147]
11.2 - 10.2 Lecture Hall Partitions [Seite 148]
11.3 - 10.3 Statistics on Ck . Sn [Seite 149]
11.4 - 10.4 Statistics on s-Inversion Sequences [Seite 150]
11.5 - 10.5 From Statistics on Ck o Sn to Statistics on In,k [Seite 151]
11.6 - 10.6 Lecture Hall Polytopes and s-Inversion Sequences [Seite 153]
11.7 - 10.7 Lecture Hall Partitions and the Inversion Sequences In,k [Seite 155]
11.8 - 10.8 A Lecture Hall Statistic on Ck . Sn [Seite 158]
11.9 - 10.9 Inflated Eulerian Polynomials for Ck . Sn [Seite 160]
11.10 - 10.10 Concluding Remarks [Seite 163]