(maxima.info)Package combinatorics

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48.1 Package combinatorics
==========================

The 'combinatorics' package provides several functions to work with
permutations and to permute elements of a list.  The permutations of
degree _n_ are all the _n_!  possible orderings of the first _n_
positive integers, 1, 2, ..., _n_.  The functions in this packages
expect a permutation to be represented by a list of those integers.

   Cycles are represented as a list of two or more integers _i_1_,
_i_2_, ..., _i_m_, all different.  Such a list represents a permutation
where the integer _i_2_ appears in the _i_1_th position, the integer
_i_3_ appears in the _i_2_th position and so on, until the integer
_i_1_, which appears in the _i_m_th position.

   For instance, [4, 2, 1, 3] is one of the 24 permutations of degree
four, which can also be represented by the cycle [1, 4, 3].  The
functions where cycles are used to represent permutations also require
the order of the permutation to avoid ambiguity.  For instance, the same
cycle [1, 4, 3] could refer to the permutation of order 6: [4, 2, 1, 3,
5, 6].  A product of cycles must be represented by a list of cycles; the
cycles at the end of the list are applied first.  For example, [[2, 4],
[1, 3, 6, 5]] is equivalent to the permutation [3, 4, 6, 2, 1, 5].

   A cycle can be written in several ways.  for instance, [1, 3, 6, 5],
[3, 6, 5, 1] and [6, 5, 1, 3] are all equivalent.  The canonical form
used in the package is the one that places the lowest index in the first
place.  A cycle with only two indices is also called a transposition and
if the two indices are consecutive, it is called an adjacent
transposition.

   To run an interactive tutorial, use the command 'demo
(combinatorics)'.  Since this is an additional package, it must be
loaded with the command 'load("combinatorics")'.