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A principle that was first enunciated by Jakob Bernoulli which states that if we are ignorant of the ways an event can occur (and therefore have no reason to believe that one ...

A multinomial series is generalization of the binomial series discovered by Johann Bernoulli and Leibniz. The multinomial series arises in a generalization of the binomial ...

First-passage percolation is a time-dependent generalization of discrete Bernoulli percolation in which each graph edge e of Z^d is assigned a nonnegative random variable ...

The series sum_(k=1)^infty1/k (1) is called the harmonic series. It can be shown to diverge using the integral test by comparison with the function 1/x. The divergence, ...

In discrete percolation theory, bond percolation is a percolation model on a regular point lattice L=L^d in d-dimensional Euclidean space which considers the lattice graph ...

A set of numbers obeying a pattern like the following: 91·37 = 3367 (1) 9901·3367 = 33336667 (2) 999001·333667 = 333333666667 (3) 99990001·33336667 = 3333333366666667 (4) 4^2 ...

By way of analogy with the eban numbers, aban numbers are defined as numbers whose English names do not contain the letter "a" (i.e., "a" is banned). Note that this ...

It is possible to construct simple functions which produce growing patterns. For example, the Baxter-Hickerson function f(n)=1/3(2·10^(5n)-10^(4n)+2·10^(3n)+10^(2n)+10^n+1) ...

The pentanacci numbers are a generalization of the Fibonacci numbers defined by P_0=0, P_1=1, P_2=1, P_3=2, P_4=4, and the recurrence relation ...

The eban numbers are the sequence of numbers whose names (in English) do not contain the letter "e" (i.e., "e" is "banned"). The name was coined by N. J. A. Sloane around ...