Surveys in Combinatorics 1985: Invited Papers for the Tenth British Combinatorial Conference (London Mathematical Society Lecture Note Series, Series Number 103)

✍ Scribed by Ian Anderson (editor)

• Publisher: Cambridge University Press
• Year: 1985
• Tongue: English
• Leaves: 180
• Edition: 1
• Category: Library

✦ Synopsis

The British Combinatorial Conference is an established biennial international gathering. This volume contains the invited papers presented, by several distinguished mathematicians, at the 1985 conference. The papers cover a broad range of combinatorial topics, including cryptography, greedy algorithms, graph minors, flows through random networks, (0, 1)-distance problems, irregularities of point distributions and reconstruction of infinite graphs.

✦ Table of Contents

Cover
Series Page
Title
Copyright
CONTENTS
PREFACE
Combinatorics and Ramanujan's 'Lost' Notebook
1. Introduction
2. The Combinatorial Setting
3. Determination of Ramanujan Statistics
4. The Third Order Mock Theta Function
5. The Fifth and Seventh Order Mock Theta Functions
6. The Sixth Order Mock Theta Functions
7. A Further Example From the 'Lost' Notebook
8. Regime II of the Hard Hexagon Model
9. Conclusion
REFERENCES
IRREGULARITIES OF DISTRIBUTION AND COMBINATORICS
1. INTRODUCTION
2. MEASURE THEORETIC DISCREPANCY
3. COMBINATORIAL DISCREPANCY
4. MISCELLANEOUS RESULTS
5. PROOF OF THEOREM 1. 9
REFERENCES
ADAPTIVE ALGORITHMS FOR COMMUNICATIONS
1. A/D and D/A
2. DSP
3. Filters
4. Equalisation
S. Modulation
6. Coding
7. Data Rates
8. Channel Selection
Conclusions
RANDOM FLOWS: NETWORK FLOWS AND ELECTRICAL FLOWS THROUGH RANDOM MEDIA
ABSTRACT
CONTENTS
1. INTRODUCTION
2. RANDOM VARIABLES AND DISTRIBUTIONS
3. NETWORK FLOWS
3.1. The problem
3.2. Capacitated networks
3.3. Random capacities
3.4. Trees
3.5. Complete graphs
3.6. Crystalline lattices
4. ELECTRICAL NETWORKS
4.1. The problem
4.2. Kirchhoff's and Ohm's laws
4.3. Random resistances
4.4. Trees
4.5. Complete graphs
4.6. Crystalline lattices
REFERENCES
ON GREEDY ALGORITHMS THAT SUCCEED
1. Introduction
2. Monge
3. Boruvka
4. Jacobs
5. Jacobs - SHORTEST PATH
6. Jacobs - SERIES PARALLEL GRAPHS
7. Some Problems
REFERENCES
{0,1,} DISTANCE PROBLEMS IN COMBINATORICS
1 INTRODUCTION
2 THE ADDRESSING PROBLEM FOR GRAPHS
2.1 Introduction, examples
2.2 A lower bound
2.3 An upper bound
2.4 Directed graphs
3 ASSOCIATIVE BLOCK DESIGNS
3.1 Introduction
3.2 Restrictions on parameters
3.3 Constructions
4 {O,l,}-TOURNAMENT CODES
4.1 Introduction
4.2 An upper bound
4.3 A lower bound
REFERENCES
DETACHMENTS OF GRAPHS AND GENERALISED EULER TRAILS
REFERENCES
GRAPH MINORS – A SURVEY
1. INTRODUCTION
2. WELL-QUASI-ORDERING
3. DISJOINT PATHS
4. STRUCTURE THEOREMS
5. CUQUE-SUMS
6. MINORS AND SURFACFS
7. APPUCATIONS TO WELL-QUASI-ORDERING
8. APPLICATIONS TO DISJOINT PATH PROBLEMS
REFERENCES
INDEX