Size of Permutation: Show building helper

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One line notation:
Cycle notation:
Two line notation:

About Permutations

In general, a permutation is a rearrangement of objects. Frequently, a permutation is represented as an arrangement of the set \(\{1,2,\ldots , n\}\), where \(n\) is a positive integer called the size of the permutation. There are \(n!\) possible permutations of this set. For instance, the 6 permutations of the set \(\{1,2,3\}\) are \(\{1,2,3\}\), \(\{1,3,2\}\), \(\{2,1,3\}\), \(\{2,3,1\}\), \(\{3,1,2\}\), \(\{3,2,1\}\). A permutation \(\pi\) is a map, and we write \(\pi(x) = y\) if \(\pi\) sends the element \(x\) to the \(y\)th position.

A permutation \(\pi\) can be described using a variety of notations, several of which are seen in this applet:
A wide range of mathematical areas make use of permutations. Algebraists might study the symmetric group \(S_n\), whose elements are the permutations on \(n\) numbers. This group has identity \(\{1, 2, 3, \ldots, n\}\) and its operation is composition. Every permutation \(\pi\) has an inverse, defined by \(\pi^{-1}(j) =i\) if \(\pi(i) = j\).

Using the Applet

Enter a permutation in one of four ways: A message will be displayed if an invalid permutation is entered. In particular, and each element of the set \(\{1, 2, \ldots, n\}\) must be used exactly once where \(n\) is the size of the permutation. The size can range from 2 to 9. When a valid permutation is entered, each notation will be displayed and some data relevant to the permutation will be displayed, including:

About this Applet

This applet was created using JavaScript and the Raphael library. If you are unable to see the applet, make sure you have JavaScript enabled in your browser. This applet may not be supported by older browsers.