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Consider a game, first proposed by Nicolaus Bernoulli, in which a player bets on how many tosses of a coin will be needed before it first turns up heads. The player pays a ...

Let alpha(G) denote the independence number of a graph G. Then the Shannon capacity Theta(G), sometimes also denoted c(G), of G is defined as ...

There are certain optimization problems that become unmanageable using combinatorial methods as the number of objects becomes large. A typical example is the traveling ...

Skewness is a measure of the degree of asymmetry of a distribution. If the left tail (tail at small end of the distribution) is more pronounced than the right tail (tail at ...

An integer is k-smooth if it has no prime factors >k. The following table gives the first few k-smooth numbers for small k. Berndt (1994, p. 52) called the 7-smooth numbers ...

Ramanujan calculated mu=1.45136380... (Hardy 1999, Le Lionnais 1983, Berndt 1994), while the correct value is mu=1.45136923488... (OEIS A070769; Derbyshire 2004, p. 114). The ...

The triakis icosahedral graph is Archimedean dual graph which is the skeleton of the triakis icosahedron. It is implemented in the Wolfram Language as ...

The triakis tetrahedral graph is Archimedean dual graph which is the skeleton of the triakis tetrahedron. It is implemented in the Wolfram Language as ...

A twin Pythagorean triple is a Pythagorean triple (a,b,c) for which two values are consecutive integers. By definition, twin triplets are therefore primitive triples. Of the ...

For a single variate X having a distribution P(x) with known population mean mu, the population variance var(X), commonly also written sigma^2, is defined as ...