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Combinatorial Number Theory: Proceedings of the Integers Conference 2011, Carrollton, Georgia, USA, October 26-29, 2011 [Hardback]

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  • Formāts: Hardback, 166 pages, height x width: 240x170 mm, weight: 425 g, 18 Illustrations, black and white
  • Sērija : De Gruyter Proceedings in Mathematics
  • Izdošanas datums: 19-Aug-2013
  • Izdevniecība: De Gruyter
  • ISBN-10: 3110280485
  • ISBN-13: 9783110280487
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Combinatorial Number Theory: Proceedings of the Integers Conference 2011, Carrollton, Georgia, USA, October 26-29, 2011Palielināt
  • Formāts: Hardback, 166 pages, height x width: 240x170 mm, weight: 425 g, 18 Illustrations, black and white
  • Sērija : De Gruyter Proceedings in Mathematics
  • Izdošanas datums: 19-Aug-2013
  • Izdevniecība: De Gruyter
  • ISBN-10: 3110280485
  • ISBN-13: 9783110280487
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9783110280487.html
Keywords:
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.
Preface v
1 The Misere Monoid of One-Handed Alternating Games
1(14)
Rebecca Milley
Richard J. Nowakowski
Paul Ottaway
1.1 Introduction
1(3)
1.1.1 Background
2(2)
1.2 Equivalences
4(6)
1.3 Outcomes
10(2)
1.4 The Misere Monoid
12(3)
2 Images of C-Sets and Related Large Sets under Nonhomogeneous Spectra
15(22)
Neil Hindman
John H. Johnson
2.1 Introduction
15(4)
2.2 The Various Notions of Size
19(6)
2.3 The Functions fα and hα
25(2)
2.4 Preservation of J-Sets, C-Sets, and C*-Sets
27(6)
2.5 Preservation of Ideals
33(4)
3 On the Differences Between Consecutive Prime Numbers, I
37(8)
Daniel A. Goldston
Andrew H. Ledoan
3.1 Introduction and Statement of Results
37(1)
3.2 The Hardy---Littlewood Prime k-Tuple Conjectures
38(1)
3.3 Inclusion---Exclusion for Consecutive Prime Numbers
39(3)
3.4 Proof of the Theorem
42(3)
4 On Sets of Integers Which Are Both Sum-Free and Product-Free
45(10)
Par Kurlberg
Jeffrey C. Lagarias
Carl Pomerance
4.1 Introduction
45(2)
4.2 The Upper Density
47(3)
4.3 An Upper Bound for the Density in Z/nZ
50(1)
4.4 Examples With Large Density
51(4)
5 Four Perspectives on Secondary Terms in the Davenport---Heilbronn Theorems
55(24)
Frank Thorne
5.1 Introduction
55(1)
5.2 Counting Fields in General
56(4)
5.2.1 Counting Torsion Elements in Class Groups
59(1)
5.3 Davenport---Heilbronn, Delone---Faddeev, and the Main Terms
60(2)
5.3.1 The Work of Belabas, Bhargava, and Pomerance
61(1)
5.4 The Four Approaches
62(1)
5.5 The Shintani Zeta-Function Approach
63(4)
5.5.1 Nonequidistribution in Arithmetic Progressions
66(1)
5.6 A Refined Geometric Approach
67(3)
5.6.1 Origin of the Secondary Term
68(1)
5.6.2 A Correspondence for Cubic Forms
69(1)
5.7 Equidistribution of Heegner Points
70(3)
5.7.1 Heegner Points and Equidistribution
71(2)
5.8 Hirzebruch Surfaces and the Maroni Invariant
73(1)
5.9 Conclusion
74(5)
6 Spotted Tilings and n-Color Compositions
79(12)
Brian Hopkins
6.1 Background
79(2)
6.2 n-Color Composition Enumerations
81(5)
6.3 Conjugable n-Color Compositions
86(5)
7 A Class of Wythoff-Like Games
91(18)
Aviezri S. Fraenkel
Yuval Tanny
7.1 Introduction
91(2)
7.2 Constant Function
93(6)
7.2.1 A Numeration System
94(4)
7.2.2 Strategy Tractability and Structure of the P-Positions
98(1)
7.3 Superadditive Functions
99(4)
7.4 Polynomial
103(3)
7.5 Further Work
106(3)
8 On the Multiplicative Order of Fn+1/Fn Modulo Fm
109(14)
Takao Komatsu
Florian Luca
Yohei Tachiya
8.1 Introduction
109(1)
8.2 Preliminary Results
110(4)
8.3 Proof of Theorem 8.1
114(6)
8.4 Comments and Numerical Results
120(3)
9 Outcomes of Partizan Euclid
123(14)
Neil A. McKay
Richard J. Nowakowski
9.1 Introduction
123(2)
9.2 Game Tree Structure
125(3)
9.3 Reducing the Signature
128(5)
9.3.1 Algorithm
132(1)
9.4 Outcome Observations
133(1)
9.5 Open Questions
134(3)
10 Lecture Hall Partitions and the Wreath Products Ck Sn
137(18)
Thomas W. Pensyl
Carla D. Savage
10.1 Introduction
137(1)
10.2 Lecture Hall Partitions
138(1)
10.3 Statistics on Ck Sn
139(1)
10.4 Statistics on s-Inversion Sequences
140(1)
10.5 From Statistics on Ck Sn to Statistics on In,k
141(2)
10.6 Lecture Hall Polytopes and s-Inversion Sequences
143(2)
10.7 Lecture Hall Partitions and the Inversion Sequences In,k
145(3)
10.8 A Lecture Hall Statistic on Ck Sn
148(2)
10.9 Inflated Eulerian Polynomials for Ck Sn
150(3)
10.10 Concluding Remarks
153(2)
Index 155
Bruce M. Landman, University of West Georgia, Carrollton, USA; Melvyn B. Nathanson, The City University of New York, Bronx, USA; Jaroslav Neetril, Charles University, Prague, Czech Republic; Richard J. Nowakowski, Dalhousie University, Halifax, Canada; Carl Pomerance, Dartmouth College, Hanover, ; Aaron Robertson, Colgate University, Hamilton, USA.