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In machine learning theory, the Vapnik-Chervonenkis dimension or VC-dimension of a concept class C is the cardinality of the largest set S which can be shattered by C. If ...

The vector triple product identity is also known as the BAC-CAB identity, and can be written in the form Ax(BxC) = B(A·C)-C(A·B) (1) (AxB)xC = -Cx(AxB) (2) = -A(B·C)+B(A·C). ...

The Wolstenholme numbers are defined as the numerators of the generalized harmonic number H_(n,2) appearing in Wolstenholme's theorem. The first few are 1, 5, 49, 205, 5269, ...

The identity element of an additive monoid or group or of any other algebraic structure (e.g., ring, module, abstract vector space, algebra) equipped with an addition. It is ...

The de Longchamps ellipse of a triangle DeltaABC is the conic circumscribed on the incentral triangle and the Cevian triangle of the isogonal mittenpunkt X_(57). (Since a ...

A k-coloring of a graph G is a vertex coloring that is an assignment of one of k possible colors to each vertex of G (i.e., a vertex coloring) such that no two adjacent ...

A k-subset is a subset of a set on n elements containing exactly k elements. The number of k-subsets on n elements is therefore given by the binomial coefficient (n; k). For ...

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 ...

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 plane partition is a two-dimensional array of integers n_(i,j) that are nonincreasing both from left to right and top to bottom and that add up to a given number n. In ...