[Python-ideas] Extremely weird itertools.permutations

[Terry Reedy]

On 10/12/2013 3:35 AM, Steven D'Aprano wrote:

> I'd even turn this around and challenge you to find a source that *does*
> define them as always unique. Here's a typical example, from the Collins
> Dictionary of Mathematics:
>
>
> [quote]
> **permutation** or **ordered arrangement** n. 1 an ordered arrangement
> of a specified number of objects selected from a set. The number of
> distinct permutations of r objects from n is
>
>      n!/(n-r)!
>
> usually written <subscript>n P <subscript>r or <superscript>n P
> <subscript>r. For example there are six distinct permutations of two
> objects selected out of three: <1,2>, <1,3>, <2,1>, <2,3>, <3,1>, <3,2>.
> Compare COMBINATION.

The items of a set are, by definition of a set, distinct, so the 
question of different but equal permutations does not arise.

> 2. any rearrangement of all the elements of a finite sequence, such as
> (1,3,2) and (3,1,2). It is *odd* or *even* according as the number of
> exchanges of position yielding it from the original order is odd or
> even. It is a *cyclic permutation* if it merely advances all the
> elements a fixed number of places; that is, if it is a CYCLE of maximal
> LENGTH. A *transposition* is a cycle of degree two, and all permutations
> factor as products of transpositions. See also SIGNATURE.

The items of a sequence may be duplicates. But in the treatments of 
permutations I have seen (admittedly not all of them), they are 
considered to be distinguished by position, so that one may replace the 
item by counts 1 to n and vice versa.

> 3. any BIJECTION of a set to itself, where the set may be finite or
> infinite.
> [end quote]

Back to a set of distinct items again.

You are correct that itertools.permutations does the right thing by 
standard definition.

> Last but not least, here's a source which clearly distinguishes
> permutations from "permutations with duplicates":
>
> http://mathcentral.uregina.ca/QQ/database/QQ.09.07/h/beth3.html
>
> and even gives a distinct formula for calculating the number of
> permutations. Neither Wolfram Mathworld nor the Collins Dictionary of
> Maths consider this formula important enough to mention, which suggests
> strongly that it should be considered separate from the default
> permutations.

The question is whether this particular variation is important inportant 
enough to put in itertools. It is not a combinatorics module and did not 
start with permutations.

-- 
Terry Jan Reedy