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An O(nlgn) sorting algorithm which is not quite as fast as quicksort. It is a "sort-in-place" algorithm and requires no auxiliary storage, which makes it particularly concise ...

A permutation which shifts all elements of a set by a fixed offset, with the elements shifted off the end inserted back at the beginning. For a set with elements a_0, a_1, ...

The decimal expansion of a number is its representation in base-10 (i.e., in the decimal system). In this system, each "decimal place" consists of a digit 0-9 arranged such ...

A face-centered cubic sphere packing obtained by placing layers of spheres one on top of another. Because there are two distinct ways to place each layer on top of the ...

Disconnectivities are mathematical entities which stand in the way of a space being contractible (i.e., shrunk to a point, where the shrinking takes place inside the space ...

Place 2n balls in a bag and number them 1 to 2n, then pick half of them at random. The number of different possible sums for n=1, 2, 3, ... are then 2, 5, 10, 17, 26, ... ...

An element of an adèle group, sometimes called a repartition in older literature (e.g., Chevalley 1951, p. 25). Adèles arise in both number fields and function fields. The ...

Gomoku, also called go-moku (Japanese for "five points") is a tic-tac-toe-like game in which two players alternately place pieces, with each player using pieces of a fixed ...

There are several different kinds of magic numbers. The digital root and magic constant are sometimes known as magic numbers. In baseball, the magic number for a team in ...

An interpretation of first-order logic consists of a non-empty domain D and mappings for function and predicate symbols. Every n-place function symbol is mapped to a function ...