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A set of ascending sequences in a permutation is called a run (Graham et al. 1994) or sometimes a rise (Comtet 1974, p. 241). A sorted permutation consists of a single run, ...

The positive integers 216 and 12960000 appear in an obscure passage in Plato's The Republic. In this passage, Plato alludes to the fact that 216 is equal to 6^3, where 6 is ...

The limiting rabbit sequence written as a binary fraction 0.1011010110110..._2 (OEIS A005614), where b_2 denotes a binary number (a number in base-2). The decimal value is ...

To define a recurring digital invariant of order k, compute the sum of the kth powers of the digits of a number n. If this number n^' is equal to the original number n, then ...

In his famous paper of 1859, Riemann stated that the number N(T) of Riemann zeta function zeros sigma+it with 0<t<=T is asymptotically given by ...

The solid angle Omega subtended by a surface S is defined as the surface area Omega of a unit sphere covered by the surface's projection onto the sphere. This can be written ...

Sphere line picking is the selection of pairs of points corresponding to vertices of a line segment with endpoints on the surface of a sphere. n random line segments can be ...

A spherical ring is a sphere with a cylindrical hole cut so that the centers of the cylinder and sphere coincide, also called a napkin ring. Let the sphere have radius R and ...

The Spieker center is the center Sp of the Spieker circle, i.e., the incenter of the medial triangle of a reference triangle DeltaABC. It is also the center of the excircles ...

The point T at which the lines through the polygon vertices of a triangle perpendicular to the corresponding sides of the first Brocard triangle, are concurrent. The Tarry ...