Info on Permutations

Information on Permutations ...

This page gives a brief explanation of the input and output options available on the "Generate Permutations" page. More extensive explanation is given on the following pages.

Permutations

A permutation of objects is an arrangement of those objects in some order; that is, some object is placed in the first position, another in the second position, and so on, until all objects have been placed. For our purposes, a permutation is a string a₁ a₂ ... a_n, where each a_i is an element of the set [n] = {1,2,...,n} and each element occurs precisely once. For example, the permutations of [3] = {1,2,3} are 123, 132, 213, 231, 312, 321.

COS can be used to generate many restricted types of permutations.

Required Input:: The number of elements n is always required.
Sometimes a second parameter k is required.
Optional Input:: For derangements k is an optional input.
Ignored Input:: None.

One line notation Oput:
Cycle notation Output:
Transposition Output:
Permutation Matrix Output:
Inverse Permutation Output:
Standard Young Tableau Output:

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