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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Hlavní autoři:	Integers Conference (2011 : Carrollton, Georgia, USA), Landman, Bruce, Nathanson, Melvyn Bernard, Nowakowski, Richard J., Nešetřil, Jaroslav, Pomerance, Carl, Robertson, Aaron
Médium:	E-kniha Kniha
Jazyk:	angličtina
Vydáno:	Germany De Gruyter 2013 De Gruyter, Inc
Vydání:	1
Edice:	De Gruyter Proceedings in Mathematics
Témata:	Combinatorial Game Combinatorial Number Theory Combinatorial number theory > Congresses Combinatorics Congresses Integers MATHEMATICS MATHEMATICS / Algebra / General MATHEMATICS / Combinatorics MATHEMATICS / Discrete Mathematics MATHEMATICS / Finite Mathematics MATHEMATICS / Number Theory MATHEMATICS / Reference MATHEMATICS / Research Number Theory Partition Ramsey Theory Integers Partition Combinatorial Game Ramsey Theory Combinatorial Number Theory Number Theory Combinatorics
ISBN:	9783110280616, 3110280612, 3110280485, 9783110280487
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Abstract	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-annually since 2003. It featured plenary lectures presented by Ken Ono, Carla Savage, Laszlo Szekely, Frank Thorne, and Julia Wolf, along with sixty other research talks. This volume consists of ten refereed articles, which are expanded and revised versions of talks presented at the conference. They represent a broad range of topics in the areas of number theory and combinatorics including multiplicative number theory, additive number theory, game theory, Ramsey theory, enumerative combinatorics, elementary number theory, the theory of partitions, and integer sequences.
AbstractList	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-annually since 2003. It featured plenary lectures presented by Ken Ono, Carla Savage, Laszlo Szekely, Frank Thorne, and Julia Wolf, along with sixty other research talks. This volume consists of ten refereed articles, which are expanded and revised versions of talks presented at the conference. They represent a broad range of topics in the areas of number theory and combinatorics including multiplicative number theory, additive number theory, game theory, Ramsey theory, enumerative combinatorics, elementary number theory, the theory of partitions, and integer sequences. These proceedings consist of several articles based on talks given at the "Integers Conference 2011" in the area of combinatorial number theory. They present a range of important and modern research topics in the areas of number, partition, combinatorial game, Ramsey, additive number, and multiplicative number theory. The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Author	Nowakowski, Richard J. Landman, Bruce Nathanson, Melvyn Bernard Pomerance, Carl Robertson, Aaron Integers Conference (2011 : Carrollton, Georgia, USA) Nešetřil, Jaroslav
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Keywords	Integers Partition Combinatorial Game Ramsey Theory Combinatorial Number Theory Number Theory Combinatorics
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Notes	Includes bibliographical references and idex Other editors: Melvyn B. Nathanson, Jaroslav Nešetřil, Richard J. Nowakowski, Carl Pomerance, Aaron Robertson
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Snippet	This volume contains selected refereed papers based on lectures presented at the "Integers Conference 2011", an international conference in combinatorial... The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a... These proceedings consist of several articles based on talks given at the "Integers Conference 2011" in the area of combinatorial number theory. They present a...
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SubjectTerms	Combinatorial Game Combinatorial Number Theory Combinatorial number theory -- Congresses Combinatorics Congresses Integers MATHEMATICS MATHEMATICS / Algebra / General MATHEMATICS / Combinatorics MATHEMATICS / Discrete Mathematics MATHEMATICS / Finite Mathematics MATHEMATICS / Number Theory MATHEMATICS / Reference MATHEMATICS / Research Number Theory Partition Ramsey Theory
Subtitle	Proceedings of the "Integers Conference 2011", Carrollton, Georgia, USA, October 26-29, 2011
TableOfContents	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 - Frank Thorne -- / 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 --
Title	Combinatorial Number Theory
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