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In general, it is possible to link two n-dimensional hyperspheres in (n+2)-dimensional space in an infinite number of inequivalent ways. In dimensions greater than n+2 in the ...

The reversal of a positive integer abc...z is z...cba. The reversal of a positive integer n is implemented in the Wolfram Language as IntegerReverse[n]. A positive integer ...

A (v,g)-cage graph is a v-regular graph of girth g having the minimum possible number of nodes. When v is not explicitly stated, the term "g-cage" generally refers to a ...

A branch point whose neighborhood of values wrap around the range a finite number of times p as their complex arguments theta varies from 0 to a multiple of 2pi is called an ...

A dimension also called the fractal dimension, Hausdorff dimension, and Hausdorff-Besicovitch dimension in which nonintegral values are permitted. Objects whose capacity ...

The number of ways to arrange n distinct objects along a fixed (i.e., cannot be picked up out of the plane and turned over) circle is P_n=(n-1)!. The number is (n-1)! instead ...

The average number of regions into which n randomly chosen planes divide a cube is N^_(n)=1/(324)(2n+23)n(n-1)pi+n+1 (Finch 2003, p. 482). The maximum number of regions is ...

The maximum number of pieces into which a cylinder can be divided by n oblique cuts is given by f(n) = (n+1; 3)+n+1 (1) = 1/6(n+1)(n^2-n+6) (2) = 1/6(n^3+5n+6), (3) where (a; ...

For the rational curve of an unperturbed system with rotation number r/s under a map T (for which every point is a fixed point of T^s), only an even number of fixed points ...

A continuous distribution in which the logarithm of a variable has a normal distribution. It is a general case of Gibrat's distribution, to which the log normal distribution ...