Landman / Nathanson / Nešetril Combinatorial Number Theory

Proceedings of the "Integers Conference 2011", Carrollton, Georgia, October 26-29, 2011
1. Auflage 2013
ISBN: 978-3-11-028061-6
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 166 Seiten

Reihe: De Gruyter Proceedings in Mathematics

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.

Zielgruppe

Graduate Students, Researchers, and Lecturers in Mathematics; Aca

Autoren/Hrsg.

Landman, Bruce

Nathanson, Melvyn B.

Nešetril, Jaroslav

Nesetril, Jaroslav

Nowakowski, Richard J.

Pomerance, Carl

Robertson, Aaron

Aaron,

Weitere Mitwirkende

Fraenkel, Aviezri S.

Goldston, Daniel A.

Hindman, Neil

Hopkins, Brian

Johnson, John H.

Komatsu, Takao

Kurlberg, Pär

Lagarias, Jeffrey C.

Ledoan, Andrew H.

Luca, Florian

McKay, Neil A.

Milley, Rebecca

Nowakowski, Richard J.

Ottaway, Paul

Pensyl, Thomas W.

Pomerance, Carl

Savage, Carla D.

Tachiya, Yohei

Tanny, Yuval

Thorne, Frank

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

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

Über Autor(innen)

Bruce M. Landman, University of West Georgia, Carrollton, USA; Melvyn B. Nathanson, The City University of New York, Bronx, USA; Jaroslav Nešetril, Charles University, Prague, Czech Republic; Richard J. Nowakowski, Dalhousie University, Halifax, Canada; Carl Pomerance, Dartmouth College, Hanover,; Aaron Robertson,Colgate University, Hamilton, USA.