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The falling factorial (x)_n, sometimes also denoted x^(n__) (Graham et al. 1994, p. 48), is defined by (x)_n=x(x-1)...(x-(n-1)) (1) for n>=0. Is also known as the binomial ...

A function is a relation that uniquely associates members of one set with members of another set. More formally, a function from A to B is an object f such that every a in A ...

The geometric distribution is a discrete distribution for n=0, 1, 2, ... having probability density function P(n) = p(1-p)^n (1) = pq^n, (2) where 0<p<1, q=1-p, and ...

A Halin graph, sometimes known as a roofless polyhedron, is a polyhedral graph constructed from a planar embedding of a tree having four or more vertices, no vertices of ...

In the early 1950s, Ernst Straus asked 1. Is every region illuminable from every point in the region? 2. Is every region illuminable from at least one point in the region? ...

Maximize the distance a Jeep can penetrate into the desert using a given quantity of fuel. The Jeep is allowed to go forward, unload some fuel, and then return to its base ...

Let f(z) be an entire function such that f(n) is an integer for each positive integer n. Then Pólya (1915) showed that if lim sup_(r->infty)(lnM_r)/r<ln2=0.693... (1) (OEIS ...

Consider the plane figure obtained by drawing each diagonal in a regular polygon with n vertices. If each point of intersection is associated with a node and diagonals are ...

A general plane quartic curve is a curve of the form (1) Examples include the ampersand curve, bean curve, bicorn, bicuspid curve, bifoliate, bifolium, bitangent-rich curve, ...

If two similar figures lie in the plane but do not have parallel sides (i.e., they are similar but not homothetic), there exists a center of similitude, also called a ...