Michael Albert, Richard Nowakowski, David Wolfe

Lessons in Play (eBook, ePUB)

An Introduction to Combinatorial Game Theory, Second Edition

• Format: ePub

Produktbeschreibung

A thorough revision of a popular text in combinatorial game theory, this second edition reorganizes presentation to make it more widely accessible.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 344
• Erscheinungstermin: 30. April 2019
• Englisch
• ISBN-13: 9780429537561
• Artikelnr.: 62172588

Autorenporträt

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