permutations

perms

permutation generator

Created by Panaiotis
© 2001 by Panaiotis. All rights reserved.

perms uses interval class transformations to generate unique permutations of unordered sets with 1 to 8 members.

	bang	in leftmost inlet: output most recent member index.
	int	in leftmost inlet: set index value. Triggers output of corresponding universal set member.
	int in1	values 1 to 8 are used to indicate the universal set size.
	int in2	interval class index. Range is 0 to MAXindex where MAXindex is determined by the universe and class size.
	int in3	octave restrain. When set to 0, perms will generate index values beyond the range of a single set membership. Turning it on (1) will restrict output to modulo universe size.
	int in4	bass member value. Determines which set member index the permutation class starts from.
	int in5	mode or rotation. Range is 0 to maxRotations where maxRotations is determined by the universe size, class size, and array index.
	int in6	normal/inverted form of the array. Has no effect if the array is non-invertible. Values are 0 (normal) and 1 (inverted).
	int in7	normal/retrograde form of the array. Has no effect if the array is symmetrical. Values are 0 (normal) and 1 (retrograde).
	U arg1	in left inlet. arg is the universe size. Range is 1 to 8.
	list	spray-type list. Like sending values to the inlets.
	analyze arg	In analysis mode (analyze 1), perms outputs descriptive information about the permutation each time a transformation value or set is changed (see output for details). In Performance mode (analyze 0), this information is suppressed to speed up performance.

none

From left to right:

	perm out	generated when perms receives an integer in left inlet. Set member index
	interval	generated when perms receives an integer in left inlet. Interval between previous output and current.
	maxNdx	one less than the number of classes for a given class size. Used to set a max limit on class index input.
	rotations	one less than the number of unique modes or cyclic rotations for the interval array. Used to set a max limit on mode input.
	invertible	0 if interval array inversion is non-unique, 1 if unique. < 1 1 1 :1 > is invertible since < -1 -1 -1 :-1 > (which is equivalent to <3 3 3 :3>) yields a unique set of permutations.
	symmetrical	0 if interval array is symmetrical, 1 if asymmetrical. The first asymmetrical permutation class array is 6-2: <1 1 2 1 4 :3>. Its retrograde form <1 1 3 4 1 :2> yields a unique set of permutations.
	elemAnal	Analysis output: member value of the subset.
	intrvlAnal	Analysis output: interval between previous member and current member.
	analNdx	Analysis output: member index position of the subset.

The unordered set {$, &, ¥, %} has 24 permutations. They can be represented by 2 permutation patterns using index interval arrays:

{$, &, ¥, %} set
{0, 1, 2, 3} indexed set
4-0 < 1 1 1 :1 > yields 8 permutations

4-1 < 1 2 3 :2 > yields 16 permutations

Each member of the permutation set can be accessed by its index position:

{n0, n1, n2, n3}.

A permutation of 4-1 with bass 2 in mode 1 will generate the permutation set:

{2, 0, 3, 1}, which references the objects: {¥, $, %, &}.

Input to perms: