Michael Albert - University of Otago Richard Nowakowski - Dalhousie University David Wolfe - Dalhousie University
Inhaltsangabe
Combinatorial Games 0.1 Basic Terminology Problems 1 Basic Techniques 1.1 Greedy 1.2 Symmetry 1.3 Parity 1.4 Give Them Enough Rope! 1.5 Strategy Stealing 1.6 Change the Game! 1.7 Case Study: Long Chains in Dots & Boxes Problems 2 Outcome Classes 2.1 Outcome Functions 2.2 Game Positions and Options 2.3 Impartial Games: Minding Your Ps and Ns 2.4 Case Study: Roll The Lawn 2.5 Case Study: Timber 2.6 Case Study: Partizan Endnim Problems 3 Motivational Interlude: Sums of Games 3.1 Sums 3.2 Comparisons 3.3 Equality and Identity 3.4 Case Study: Domineering Rectangles Problems 4 The Algebra of Games 4.1 The Fundamental Definitions 4.2 Games Form a Group with a Partial Order 4.3 Canonical Form 4.4 Case Study: Cricket Pitch 4.5 Incentives Problems 5 Values of Games 5.1 Numbers 5.2 Case Study: Shove 5.3 Stops 5.4 A Few All-Smalls: Up, Down, and Stars 5.5 Switches 5.6 Case Study: Elephants & Rhinos 5.7 Tiny and Miny 5.8 Toppling Dominoes 5.9 Proofs of Equivalence of Games and Numbers Problems 6 Structure 6.1 Games Born by Day 2 6.2 Extremal Games Born By Day n 6.3 More About Numbers 6.4 The Distributive Lattice of Games Born by Day n 6.5 Group Structure Problems 7 Impartial Games 7.1 A Star-Studded Game 7.2 The Analysis of Nim 7.3 Adding Stars 7.4 A More Succinct Notation 7.5 Taking-and-Breaking Games 7.6 Subtraction Games 7.7 Keypad Games Problems 8 Hot Games 8.1 Comparing Games and Numbers 8.2 Coping with Confusion 8.3 Cooling Things Down 8.4 Strategies for Playing Hot Games 8.5 Norton Products Problems 9 All-Small Games 9.1 Cast of Characters 9.2 Motivation: The Scale of Ups 9.3 Equivalence Under 9.4 Atomic Weight 9.5 All-Small Shove 9.6 More Toppling Dominoes 9.7 Clobber Problems 10 Trimming Game Trees 10.1 Introduction 10.2 Reduced Canonical Form 10.3 Hereditary-Transitive Games 10.4 Ordinal Sum 10.5 Stirling-Shave 10.6 Even More Toppling Dominoes Problems Further Directions 1 Transfinite Games 2 Algorithms and Complexity 3 Loopy Games 4 Kos: Repeated Local Positions 5 Top-Down Thermography 6 Enriched Environments 7 Idempotents 8 Mis`ere Play 9 Scoring Games A Top-Down Induction A.1 Top-Down Induction A.2 Examples
Combinatorial Games 0.1 Basic Terminology Problems 1 Basic Techniques 1.1 Greedy 1.2 Symmetry 1.3 Parity 1.4 Give Them Enough Rope! 1.5 Strategy Stealing 1.6 Change the Game! 1.7 Case Study: Long Chains in Dots & Boxes Problems 2 Outcome Classes 2.1 Outcome Functions 2.2 Game Positions and Options 2.3 Impartial Games: Minding Your Ps and Ns 2.4 Case Study: Roll The Lawn 2.5 Case Study: Timber 2.6 Case Study: Partizan Endnim Problems 3 Motivational Interlude: Sums of Games 3.1 Sums 3.2 Comparisons 3.3 Equality and Identity 3.4 Case Study: Domineering Rectangles Problems 4 The Algebra of Games 4.1 The Fundamental Definitions 4.2 Games Form a Group with a Partial Order 4.3 Canonical Form 4.4 Case Study: Cricket Pitch 4.5 Incentives Problems 5 Values of Games 5.1 Numbers 5.2 Case Study: Shove 5.3 Stops 5.4 A Few All-Smalls: Up, Down, and Stars 5.5 Switches 5.6 Case Study: Elephants & Rhinos 5.7 Tiny and Miny 5.8 Toppling Dominoes 5.9 Proofs of Equivalence of Games and Numbers Problems 6 Structure 6.1 Games Born by Day 2 6.2 Extremal Games Born By Day n 6.3 More About Numbers 6.4 The Distributive Lattice of Games Born by Day n 6.5 Group Structure Problems 7 Impartial Games 7.1 A Star-Studded Game 7.2 The Analysis of Nim 7.3 Adding Stars 7.4 A More Succinct Notation 7.5 Taking-and-Breaking Games 7.6 Subtraction Games 7.7 Keypad Games Problems 8 Hot Games 8.1 Comparing Games and Numbers 8.2 Coping with Confusion 8.3 Cooling Things Down 8.4 Strategies for Playing Hot Games 8.5 Norton Products Problems 9 All-Small Games 9.1 Cast of Characters 9.2 Motivation: The Scale of Ups 9.3 Equivalence Under 9.4 Atomic Weight 9.5 All-Small Shove 9.6 More Toppling Dominoes 9.7 Clobber Problems 10 Trimming Game Trees 10.1 Introduction 10.2 Reduced Canonical Form 10.3 Hereditary-Transitive Games 10.4 Ordinal Sum 10.5 Stirling-Shave 10.6 Even More Toppling Dominoes Problems Further Directions 1 Transfinite Games 2 Algorithms and Complexity 3 Loopy Games 4 Kos: Repeated Local Positions 5 Top-Down Thermography 6 Enriched Environments 7 Idempotents 8 Mis`ere Play 9 Scoring Games A Top-Down Induction A.1 Top-Down Induction A.2 Examples
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