Index

In this index, references to the deﬁnitions of terminology are

printed using boldface page numbers. References to primary

statements or proofs of theorems are printed using italic page

numbers.

A, B, C Property, 320

Abelian group, 459

cyclic, 460

direct product, 460

divisible, 461

ﬁnitely generated, 460

quotient, 460

torsion, 460

torsion-free, 460

absorbs, 470

Ackermann function, 39

activation temperature, 360

active, 342, 359, 360, 364, 387

adjoint, 270

aﬃne stratiﬁcation, 269

algebraic periodic, 269

algorithmic combinatorial game theory,

44–46

all-moderate, 405, 406, 412

all-small, 63, 405, 406, see also dicotic

alternating game, 82

in mis`ere play, 278

annihilation game, 214, 489

antichain, 154, 167, 463

Archimedean Principle, 71, 156, 403

inﬁnitesimal analogue, 85, 156

arithmetic periodic, 187, 194, 196–197, 203

atomic, 142, 143–144, 149

atomic value, 151

atomic weight, 97, 136, 142, 140–146

and liberty counts in Go, 49

galvanized, 150

of a stopper, 298–299, 307

of Hackenbush positions, 149

transﬁnite, 409

atomic weight calculus, 144–146

Austin’s Theorem, 196

Avoider–Enforcer convention, see play

convention, reverse weak win

Bach’s Carousel, 315, 316, 319

balloon trajectory, 367, 368

base, 365

Berlekamp’s Sign-Expansion Rule, 421

bigraph, 281

negative, 281

binary game, 277

Binary Normal Form Theorem, 468

Birkhoﬀ’s Theorem, 465

birthday, 60, 61–62, 71, 153, 400, 421

formal, 61, 398

of a number, 72–73

board (positional game), 42

Boolean algebra, see lattice, Boolean

Bouton’s Theorem, 3, 4, 20, 35, 85, 180,

224, 236, 254, 438, 491

Mis`ere Version, 225

bynumber, 149

bypass, 65

canonical, 336

canonical form, 64, 66, 67, 68

for ﬁnite loopy games, 317

for stoppers, 305

515