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The word quantile has no fewer than two distinct meanings in probability. Specific elements x in the range of a variate X are called quantiles, and denoted x (Evans et al. ...

A rolling polyhedron graph is a graph obtained by rolling a polyhedral solid along a board whose tiles match up with the faces of the polyhedron being rolled. The vertices of ...

The Krohn-Rhodes complexity, also called the group complexity or simply "the complexity," of a finite semigroup S is the smallest number of groups in a wreath product of ...

Krohn-Rhodes theory is a mathematical approach that seeks to decompose finite semigroups in terms of finite aperiodic semigroups and finite groups.

A Lyndon word is an aperiodic notation for representing a necklace.

In Kepler's 1619 book Harmonice Mundi on tilings, he discussed a tiling built with pentagons, pentagrams, decagons, and "fused decagon pairs." He also called them "monsters." ...

A polynomial is said to be irreducible if it cannot be factored into nontrivial polynomials over the same field. For example, in the field of rational polynomials Q[x] (i.e., ...

Wolfram (2002, p. 123) considered the sequence related to the Collatz problem obtained by iterating w_n={3/2w_(n-1) for w_(n-1) even; 3/2(w_(n-1)+1) for w_(n-1) odd (1) ...

Tiling of a Möbius strip can be performed immediately by carrying over a tiling of a rectangle with the same two-sided surface area. However, additional tilings are possible ...

A tessellation which can be thought of consisting of a number of pieces which are hinged at their vertices and therefore can be opened or closed to yield a series of ...