# UNICYCLE Permutations with a Single Cycle

UNICYCLE is a Python library which carries out some operations on permutations with a single cycle.

A permutation with a single cycle is a permutation P of N objects with the property that, for every object, it takes exactly N applications of P to restore an object to its original value.

Another way to think of this is that a permutation with a single cycle can be symbolized by a bracelet with N beads; the action of the permutation is to rotate the bracelet one position.

A permutation with a single cycle can be written in "sequence" form. Assuming the objects are labeled 1 through N, we start with 1, followed by P(1), followed by P(P(1)), and so on. Thus, the sequence (1,4,2,5,3) indicates the permutation which maps 1->4, 2->5, 3->1, 4->2, and 5->3.

A permutation with a single cycle is sometimes called a "cyclic permutation", but this term is also used with other meanings. Hence, we will affectionately call these objects "unicycles".

### Languages:

UNICYCLE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

### Related Data and Programs:

SUBSET, a Python library which generates, ranks and unranks various combinatorial objects.

### Examples and Tests:

You can go up one level to the Python source codes.

Last revised on 26 August 2015.