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Let v be a n-vector whose entries are each 1 (with probability p) or 0 (with probability q=1-p). An s-run is an isolated group of s consecutive 1s. Ignoring the boundaries, ...

The Van Lint-Schrijver Graph graph is a weakly regular Hamiltonian graph on 162 vertices with parameters (nu,k,lambda,mu)=(162,(6),(0),(0,1)). It is distance-regular with ...

The eight Gell-Mann matrices lambda_i, i=1,...,8, are an example of the set of generators of the Lie algebra associated to the special unitary group SU(3). Explicitly, these ...

Let K be a number field with r_1 real embeddings and 2r_2 imaginary embeddings and let r=r_1+r_2-1. Then the multiplicative group of units U_K of K has the form ...

A (p,q)-torus knot is obtained by looping a string through the hole of a torus p times with q revolutions before joining its ends, where p and q are relatively prime. A ...

An object is unique if there is no other object satisfying its defining properties. An object is said to be essentially unique if uniqueness is only referred to the ...

In elementary geometry, orthogonal is the same as perpendicular. Two lines or curves are orthogonal if they are perpendicular at their point of intersection. Two vectors v ...

The above topological structure, composed of a countable union of compact sets, is called Alexander's horned sphere. It is homeomorphic with the ball B^3, and its boundary is ...

There are at least two statements which go by the name of Artin's conjecture. If r is any complex finite-dimensional representation of the absolute Galois group of a number ...

The Barnes-Wall lattice is a d-dimensional lattice that exists when d is a power of 2. It is implemented in the Wolfram Language as LatticeData[{"BarnesWall", n}]. Special ...