Combinatorial Game Theory: A Special Collection in Honor of Elwyn Berlekamp, John H. Conway and Richard K. Guy (De Gruyter Proceedings in Mathematics)

Elwyn Berlekamp, John Conway, and Richard Guy wrote ‘Winning Ways for your Mathematical Plays’ and turned a recreational mathematics topic into a full mathematical fi eld. They combined set theory, combinatorics, codes, algorithms, and a smattering of other fi elds, leavened with a liberal dose of humor and wit. Their legacy is a lively fi eld of study that still produces many surprises. Despite being experts in other areas of mathematics, in the 50 years since its publication, they also mentored, talked, and played games, giving their time, expertise, and guidance to several generations of mathematicians. This volume is dedicated to Elwyn Berlekamp, John Conway, and Richard Guy. It includes 20 contributions from colleagues that refl ect on their work in combinatorial game theory. * Original contributions by leading experts in combinatoric game theory. * Commemorates the work done by Professors‘ Berlekamp, Conway and Guy. * Of interest to researchers and graduate students working in combinatoric game theory Preface Contents The game of flipping coins The game of blocking pebbles Transverse Wave: an impartial color-propagation game inspired by social influence and Quantum Nim A note on numbers Ordinal sums, clockwise hackenbush, and domino shave Advances in finding ideal play on poset games Strings-and-Coins and Nimstring are PSPACE-complete Partizan subtraction games Circular Nim games CN(7, 4) Misère domineering on 2 × n boards Relator games on groups Playing Bynum’s game cautiously Genetically modified games Game values of arithmetic functions A base-p Sprague–Grundy-type theorem for p-calm subtraction games: Welter’s game and representations of generalized symmetric groups Recursive comparison tests for dicot and dead-ending games under misère play Impartial games with entailing moves Extended Sprague–Grundy theory for locally finite games, and applications to random game-trees Grundy numbers of impartial three-dimensional chocolate-bar games On the structure of misère impartial games The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications This volume is dedicated to the work of three leading mathematicians in combinatoric game theory, Elwyn Berlekamp, John Conway, and Richard Guy and includes 20 contributions from colleagues reflecting on their work.