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A set of n variables which fix a geometric object. If the coordinates are distances measured along perpendicular axes, they are known as Cartesian coordinates. The study of ...

A graph is called cordial if it is possible to label its vertices with 0s and 1s so that when the edges are labeled with the difference of the labels at their endpoints, the ...

For a subgroup H of a group G and an element x of G, define xH to be the set {xh:h in H} and Hx to be the set {hx:h in H}. A subset of G of the form xH for some x in G is ...

The cototient of a positive number n is defined as n-phi(n), where n is the totient function. It is therefore the number of positive integers <=n that have at least one prime ...

Let X be a set and S a collection of subsets of X. A set function mu:S->[0,infty] is said to possess countable monotonicity provided that, whenever a set E in S is covered by ...

A family gamma of nonempty subsets of X whose union contains the given set X (and which contains no duplicated subsets) is called a cover (or covering) of X. For example, ...

An infinite sequence of circles such that every four consecutive circles are mutually tangent, and the circles' radii ..., R_(-n), ..., R_(-1), R_0, R_1, R_2, R_3, R_4, ..., ...

A recursively enumerable set A is creative if its complement is productive. Creative sets are not recursive. The property of creativeness coincides with completeness. Namely, ...

A nonplanar graph G is said to be critical nonplanar if the removal of a vertex results in a planar graph for every vertex of G. Critical nonplanar graphs differ from apex ...

A cross-handle is a topological structure which can be thought of as the object produced by puncturing a surface twice, attaching a zip around each puncture travelling in the ...