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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 ...

Several different types of checkerboards are used in different variants of the game of checkers. The usual checkerboard is the one used in so-called "pool checkers," also ...

The first type of tensor-like object derived from a Riemannian metric g which is used to study the geometry of the metric. Christoffel symbols of the first kind are variously ...

The ditrigonal dodecadodecahedron, also called the ditrigonal dodecahedron, is the uniform polyhedron with Maeder index 41 (Maeder 1997), Wenninger index 80 (Wenninger 1989), ...

A technique in set theory invented by P. Cohen (1963, 1964, 1966) and used to prove that the axiom of choice and continuum hypothesis are independent of one another in ...

Lattice theory is the study of sets of objects known as lattices. It is an outgrowth of the study of Boolean algebras, and provides a framework for unifying the study of ...

The lower central series of a Lie algebra g is the sequence of subalgebras recursively defined by g_(k+1)=[g,g_k], (1) with g_0=g. The sequence of subspaces is always ...

The logarithmic capacity of a compact set E in the complex plane is given by gamma(E)=e^(-V(E)), (1) where V(E)=inf_(nu)int_(E×E)ln1/(|u-v|)dnu(u)dnu(v), (2) and nu runs over ...

Two lines in two-dimensional Euclidean space are said to be parallel if they do not intersect. In three-dimensional Euclidean space, parallel lines not only fail to ...

Let n be a positive integer and r(n) the number of (not necessarily distinct) prime factors of n (with r(1)=0). Let O(m) be the number of positive integers <=m with an odd ...