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The symmetric group S_n of degree n is the group of all permutations on n symbols. S_n is therefore a permutation group of order n! and contains as subgroups every group of ...

The tetragonal trapezohedron is the dual of the square antiprism. For a square antiprism with unit edge lengths, the edge lengths of the corresponding tetragonal ...

The Thue-Morse constant, also called the parity constant, is given by the concatenated digits of the Thue-Morse sequence P=0.0110100110010110100101100..._2 (1) (OEIS A010060) ...

The closure of a set A is the smallest closed set containing A. Closed sets are closed under arbitrary intersection, so it is also the intersection of all closed sets ...

A sequence of moves (i.e., a path) on a chessboard by a chess piece in which each square of a chessboard is visited exactly once.

The triangular cupola is Johnson solid J_3. Its faces consist of 4 equilateral triangles, 3 squares, and 1 hexagon. It is implemented in the Wolfram Language as ...

The tridiminished icosahedron is Johnson solid J_(63). Interestingly, its skeleton has the same degree sequence as the triangular cupola.

The function defined by U(n)=(n!)^(n!). The values for n=0, 1, ..., are 1, 1, 4, 46656, 1333735776850284124449081472843776, ... (OEIS A046882).

The function defined by U(p)=(p#)^(p#), where p is a prime number and p# is a primorial. The values for p=2, 3, ..., are 4, 46656, ...

A sequence of numbers alpha_n is said to be uncorrelated if it satisfies lim_(n->infty)1/(2n)sum_(m=-n)^nalpha_m^2=1 lim_(n->infty)1/(2n)sum_(m=-n)^nalpha_malpha_(k+m)=0 for ...