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A random composition of a number n in k parts is one of the (n+k-1; n) possible compositions of n, where (n; k) is a binomial coefficient. A random composition can be given ...

The real axis is the line in the complex plane corresponding to zero imaginary part, I[z]=0. Every real number corresponds to a unique point on the real axis.

A curvilinear polygon built up of circular arcs. The Reuleaux polygon is a generalization of the Reuleaux triangle and, for an odd number of sides, is a curve of constant ...

An algorithm for multiplying two 32-bit integers modulo a 32-bit constant without using any intermediates larger than 32 bits. It is also useful in certain types of random ...

Let a sequence {a_i}_(i=1)^infty be strictly increasing and composed of nonnegative integers. Call A(x) the number of terms not exceeding x. Then the density is given by ...

The position of a rational number in the sequence 1/1, 1/2, 2/1, 1/3, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ..., ordered in terms of increasing numerator+denominator.

A set function is a function whose domain is a collection of sets. In many instances in real analysis, a set function is a function which associates an affinely extended real ...

Let v(G) be the number of vertices in a graph G and h(G) the length of the maximum cycle in G. Then the shortness exponent of a class of graphs G is defined by sigma(G)=lim ...

A 3-multiperfect number P_3. Six sous-doubles are known (120, 672, 523776, 459818240, 1476304896, and 51001180160; OEIS A005820), and these are believed to comprise all ...

A 4-multiperfect number P_4. 36 sous-triples are known (30240, 32760, 2178540, 23569920, ...; OEIS A027687), and these are believed to comprise all sous-triples.