Combinatorial Number Theory Proceedings of the "Integers Conference 2011", Carrollton, Georgia, USA, October 26-29, 2011
This volume contains selected refereed papers based on lectures presented at the "Integers Conference 2011", an international conference in combinatorial number theory that was held in Carrollton, Georgia, United States in October 2011. This was the fifth Integers Conference, held bi-annua...
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| Main Authors: | , , , , , , |
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| Format: | eBook Book |
| Language: | English |
| Published: |
Germany
De Gruyter
2013
De Gruyter, Inc |
| Edition: | 1 |
| Series: | De Gruyter Proceedings in Mathematics |
| Subjects: | |
| ISBN: | 9783110280616, 3110280612, 3110280485, 9783110280487 |
| Online Access: | Get full text |
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Table of Contents:
- Intro -- 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
- Takao Komatsu, Florian Luca, Yohei Tachiya --
- Pär Kurlberg, Jeffrey C. Lagarias, Carl Pomerance --
- Aviezri S. Fraenkel, Yuval Tanny --
- Index
- Neil A. McKay, Richard J. Nowakowski --
- Thomas W. Pensyl, Carla D. Savage --
- Preface
- Chapter 9: Outcomes of Partizan Euclid
- Neil Hindman, John H. Johnson --
- Chapter 4 On Sets of Integers Which Are Both Sum-Free and Product-Free
- Chapter 7: A Class of Wythoff-Like Games
- Chapter 5: Four Perspectives on Secondary Terms in the Davenport–Heilbronn Theorems
- Chapter 1: The Misère Monoid of One-Handed Alternating Games
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- Frank Thorne --
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- Chapter 3: On the Differences Between Consecutive Prime Numbers, I
- Chapter 2: Images of C-Sets and Related Large Sets under Nonhomogeneous Spectra
- Contents
- Rebecca Milley, Richard J. Nowakowski, Paul Ottaway --
- Brian Hopkins --
- Chapter 6: Spotted Tilings and n-Color Compositions
- Frontmatter --
- Chapter 8: On the Multiplicative Order of Fn+1/Fn Modulo Fm
- Chapter 10: Lecture Hall Partitions and the Wreath Products Ck ≀ Sn
- Daniel A. Goldston, Andrew H. Ledoan --