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Serre's problem, also called Serre's conjecture, asserts that the implication "free module ==> projective module" can be reversed for every module over the polynomial ring ...

The Grötzsch graph is smallest triangle-free graph with chromatic number four. It is identical to the Mycielski graph of order four, and is implemented as ...

The Schur number S(k) is the largest integer n for which the interval [1,n] can be partitioned into k sum-free sets (Fredricksen and Sweet 2000). S(k) is guaranteed to exist ...

A closed sentential formula is a sentential formula in which none of the variables are free (i.e., all variables are bound). Examples of closed sentential formulas are given ...

A Chaitin's constant, also called a Chaitin omega number, introduced by Chaitin (1975), is the halting probability of a universal prefix-free (self-delimiting) Turing ...

A set of planes sharing a point in common. For planes specified in Hessian normal form, a bundle of planes can therefore be specified as ...

A formula of first-order logic is said to be in Skolemized form (sometimes also called Skolem standard form or universal form) if it is of the form forall x_1... forall x_nM, ...

On a Riemannian manifold M, there is a canonical connection called the Levi-Civita connection (pronounced lē-vē shi-vit-e), sometimes also known as the Riemannian connection ...

Connecting the centers of touching spheres in a three-dimensional Apollonian gasket by edges given a graph known as the Apollonian network. This process is illustrated above ...

A Lucas cube graph of order n is a graph that can be defined based on the n-Fibonacci cube graph by forbidding vertex strings that have a 1 both in the first and last ...