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Ramanujan developed a number of interesting closed-form expressions for generalized continued fractions. These include the almost integers ...

A uniform distribution, sometimes also known as a rectangular distribution, is a distribution that has constant probability. The probability density function and cumulative ...

The Alexander polynomial is a knot invariant discovered in 1923 by J. W. Alexander (Alexander 1928). The Alexander polynomial remained the only known knot polynomial until ...

An order-n Costas array is a permutation on {1,...,n} such that the distances in each row of the triangular difference table are distinct. For example, the permutation ...

Given a pick-7 lottery with 23 numbers that pays a prize to anyone matching at least 4 of the 7 numbers, there is a set of 253 tickets that guarantees a win. This set ...

Clebsch-Gordan coefficients are mathematical symbol used to integrate products of three spherical harmonics. Clebsch-Gordan coefficients commonly arise in applications ...

The disdyakis triacontahedral graph is Archimedean dual graph which is the skeleton of the disdyakis triacontahedron. It is implemented in the Wolfram Language as ...

The Grassmannian Gr(n,k) is the set of k-dimensional subspaces in an n-dimensional vector space. For example, the set of lines Gr(n+1,1) is projective space. The real ...

An injective module is the dual notion to the projective module. A module M over a unit ring R is called injective iff whenever M is contained as a submodule in a module N, ...

Keller conjectured that tiling an n-dimensional space with n-dimensional hypercubes of equal size yields an arrangement in which at least two hypercubes have an entire ...