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When referring to a planar object, "free" means that the object is regarded as capable of being picked up out of the plane and flipped over. As a result, mirror images are ...

A group action G×X->X is called free if, for all x in X, gx=x implies g=I (i.e., only the identity element fixes any x). In other words, G×X->X is free if the map G×X->X×X ...

This is sometimes knows as the "bars and stars" method. Suppose a recipe called for 5 pinches of spice, out of 9 spices. Each possibility is an arrangement of 5 spices ...

The generalized diameter is the greatest distance between any two points on the boundary of a closed figure. The diameter of a subset E of a Euclidean space R^n is therefore ...

The graph neighborhood of a vertex v in a graph is the set of all the vertices adjacent to v including v itself. More generally, the ith neighborhood of v is the set of all ...

A group automorphism is an isomorphism from a group to itself. If G is a finite multiplicative group, an automorphism of G can be described as a way of rewriting its ...

The group direct sum of a sequence {G_n}_(n=0)^infty of groups G_n is the set of all sequences {g_n}_(n=0)^infty, where each g_n is an element of G_n, and g_n is equal to the ...

A continuum is hereditarily decomposable if each of its subcontinua is decomposable. An interval is hereditarily decomposable, as is a circle, whereas the buckethandle (also ...

Two figures are homothetic if they are related by an expansion or geometric contraction. This means that they lie in the same plane and corresponding sides are parallel; such ...

A riffle shuffle, in which the top half of the deck is placed in the left hand, and cards are then alternatively interleaved from the left and right hands. Using an ...