Search Results for ""

Let X be a set and S a collection of subsets of X. A subset A subset X is shattered by S if each subset B subset A of A can be expressed as the intersection of A with a ...

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 ...

Let lambda_(m,n) be Chebyshev constants. Schönhage (1973) proved that lim_(n->infty)(lambda_(0,n))^(1/n)=1/3. (1) It was conjectured that the number ...

The first of the Hardy-Littlewood conjectures. The k-tuple conjecture states that the asymptotic number of prime constellations can be computed explicitly. In particular, ...

A (-1,0,1)-matrix is a matrix whose elements consist only of the numbers -1, 0, or 1. The number of distinct (-1,0,1)-n×n matrices (counting row and column permutations, the ...

A well-covered graph is a graph for which every minimal vertex cover has the same size, which is equivalent to every maximal independent vertex set being the same size. It is ...

Let N steps of equal length be taken along a line. Let p be the probability of taking a step to the right, q the probability of taking a step to the left, n_1 the number of ...

Triskaidekaphobia is the fear of 13, a number commonly associated with bad luck in Western culture. While fear of the number 13 can be traced back to medieval times, the word ...

A factor of a polynomial P(x) of degree n is a polynomial Q(x) of degree less than n which can be multiplied by another polynomial R(x) of degree less than n to yield P(x), ...

The Löwenheim-Skolem theorem is a fundamental result in model theory which states that if a countable theory has a model, then it has a countable model. Furthermore, it has a ...