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Rubik's graph is the Cayley graph of Rubik's group. The graph diameter of this graph is sometimes known as God's number, and was shown in Aug. 2010 to be equal to 20 (Rokicki ...

The complex lattice Lambda_6^omega corresponding to real lattice K_(12) having the densest hypersphere packing (kissing number) in twelve dimensions. The associated ...

Let G be a subgroup of the modular group Gamma. Then an open subset R_G of the upper half-plane H is called a fundamental region of G if 1. No two distinct points of R_G are ...

A projective space is a space that is invariant under the group G of all general linear homogeneous transformation in the space concerned, but not under all the ...

A magic square that remains magic when its border is removed. A nested magic square remains magic after the border is successively removed one ring at a time. An example of a ...

A derivation is a sequence of steps, logical or computational, from one result to another. The word derivation comes from the word "derive." "Derivation" can also refer to a ...

A module M over a unit ring R is called faithfully flat if the tensor product functor - tensor _RM is exact and faithful. A faithfully flat module is always flat and ...

Given a nonzero finitely generated module M over a commutative Noetherian local ring R with maximal ideal M and a proper ideal I of R, the Hilbert-Samuel function of M with ...

A set of n magic circles is a numbering of the intersections of the n circles such that the sum over all intersections is the same constant for all circles. The above sets of ...

Over a small neighborhood U of a manifold, a vector bundle is spanned by the local sections defined on U. For example, in a coordinate chart U with coordinates (x_1,...,x_n), ...