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Quicksort is the fastest known comparison-based sorting algorithm (on average, and for a large number of elements), requiring O(nlgn) steps. Quicksort is a recursive ...

An ambiguous figure in which the brain switches between seeing a rabbit and a duck. The duck-rabbit was "originally noted" by American psychologist Joseph Jastrow (Jastrow ...

The word "rank" refers to several related concepts in mathematics involving graphs, groups, matrices, quadratic forms, sequences, set theory, statistics, and tensors. In ...

Let G be a graph, and suppose each edge of G is independently deleted with fixed probability 0<=p<=1. Then the probability that no connected component of G is disconnected as ...

There are a number of equations known as the Riccati differential equation. The most common is z^2w^('')+[z^2-n(n+1)]w=0 (1) (Abramowitz and Stegun 1972, p. 445; Zwillinger ...

The roots (sometimes also called "zeros") of an equation f(x)=0 are the values of x for which the equation is satisfied. Roots x which belong to certain sets are usually ...

When discussing a rotation, there are two possible conventions: rotation of the axes, and rotation of the object relative to fixed axes. In R^2, consider the matrix that ...

The score sequence of a tournament is a monotonic nondecreasing sequence of the outdegrees of the graph vertices of the corresponding tournament graph. Elements of a score ...

The small rhombicuboctahedral graph is a quartic graph on 24 nodes and 48 edges that corresponds to the skeleton of the small rhombicuboctahedron. It has graph diameter 5, ...

Taking a connected graph or network with a high graph diameter and adding a very small number of edges randomly, the diameter tends to drop drastically. This is known as the ...