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Two open manifolds M and M^' are cobordant if there exists a manifold with boundary W^(n+1) such that an acceptable restrictive relationship holds.

The converse of Fisher's theorem.

A theorem that guarantees that the trajectory of Langton's ant is unbounded.

Two lines that lie on top of one another are called coincident lines.

An abbreviation for the cokernel.

The logarithm of the reciprocal of a number, equal to the negative of the logarithm of the number itself, cologx=log(1/x)=-logx.

An m×1 matrix [a_(11); a_(21); |; a_(m1)].

Combinatorial game theory is the theory of two-player games of perfect knowledge such as go, chess, or checkers.

The value of b, where a=b (mod m), taken to be nonnegative and smaller than m.

A ring is commutative if the multiplication operation is commutative.