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A coloring of plane regions, link segments, etc., is an assignment of a distinct labeling (which could be a number, letter, color, etc.) to each component. Coloring problems ...

The number of ways of picking k unordered outcomes from n possibilities. Also known as the binomial coefficient or choice number and read "n choose k," _nC_k=(n; ...

Consider a combination lock consisting of n buttons that can be pressed in any combination (including multiple buttons at once), but in such a way that each number is pressed ...

Let K subset V subset S^3 be a knot that is geometrically essential in a standard embedding of the solid torus V in the three-sphere S^3. Let K_1 subset S^3 be another knot ...

A tool with two arms joined at their ends which can be used to draw circles. In geometric constructions, the classical Greek rules stipulate that the compass cannot be used ...

Given a set S with a subset E, the complement (denoted E^' or E^_) of E with respect to S is defined as E^'={F:F in S,F not in E}. (1) Using set difference notation, the ...

If k is the elliptic modulus of an elliptic integral or elliptic function, then k^'=sqrt(1-k^2) (1) is called the complementary modulus. Complete elliptic integrals with ...

The complete products of a Boolean algebra of subsets generated by a set {A_k}_(k=1)^p of cardinal number p are the 2^p Boolean functions B_1B_2...B_p=B_1 intersection B_2 ...

If the four points making up a quadrilateral are joined pairwise by six distinct lines, a figure known as a complete quadrangle results. A complete quadrangle is therefore a ...

A sequence of numbers V={nu_n} is complete if every positive integer n is the sum of some subsequence of V, i.e., there exist a_i=0 or 1 such that n=sum_(i=1)^inftya_inu_i ...