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Let M be a regular surface with v_(p),w_(p) points in the tangent space M_(p) of M. Then the third fundamental form is given by III(v_(p),w_(p))=S(v_(p))·S(w_(p)), where S is ...

A three-colorable graph G is a graph with chromatic number chi(G)<=3.

The operation of multiplication, i.e., a times b. Various notations are a×b, a·b, a*b, ab, and (a)(b). The "multiplication sign" × is based on Saint Andrew's cross (Bergamini ...

A totative is a positive integer less than or equal to a number n which is also relatively prime to n, where 1 is counted as being relatively prime to all numbers. The number ...

An ordering of permutations in which each two adjacent permutations differ by the transposition of two elements. For the permutations of {1,2,3} there are two listings which ...

An optimal filter used for the removal of noise from a signal which is corrupted by the measuring process itself.

Two sets T_1 and T_2 are called Wilf equivalent if they belong to the same Wilf class.

An n-dimensional vector, i.e., a vector (x_1, x_2, ..., x_n) with n components. In dimensions n greater than or equal to two, vectors are sometimes considered synonymous with ...

A closed box composed of three pairs of rectangular faces placed opposite each other and joined at right angles to each other, also known as a rectangular parallelepiped. The ...

The curlicue fractal is a figure obtained by the following procedure. Let s be an irrational number. Begin with a line segment of unit length, which makes an angle phi_0=0 to ...