Implement multimajor index for permutations

[25shriya]

We add an implementation for the multimajor index
of a permutation with respect to a combination of
the same size, as described in:

Armin Jöllenbeck and Manfred Schocker. Cyclic
characters of symmetric groups. J. Algebraic Combin.,
12 (2000), 155-161. doi:10.1023/A:1026592027019

Component: combinatorics

Keywords: permutations, major index, days114/club

Author: Amrutha P, Shriya M, Divya Aggarwal, Aritra Bhattacharya

Branch/Commit: 9a93d1d

Reviewer: Amrutha P, Aritra Bhattacharya, Julian Rüth, Samuel Lelièvre

Issue created by migration from https://trac.sagemath.org/ticket/34373

[25shriya]

Branch: u/gh-25shriya/34373

[25shriya]

New commits:

2cb5411

Add multimajor index

[25shriya]

Changed author from Amrutha P to Amrutha P, Shriya M, Divya Aggarwal

[25shriya]

Commit: 2cb5411

[aggarwaldivya]

Changed keywords from partitions, major index to permutations, major index

[fchapoton]

comment:3

File "sage/combinat/permutation.py", line 3384, in sage.combinat.permutation.Permutation.multi_major_index
Failed example:
    Permutation([5, 6, 2, 1, 3, 7, 4]).multi_major_index(Composition([3, 2, 2]))
Exception raised:
    Traceback (most recent call last):
      File "/__w/sagetrac-mirror/sagetrac-mirror/src/sage/doctest/forker.py", line 695, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/__w/sagetrac-mirror/sagetrac-mirror/src/sage/doctest/forker.py", line 1093, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.combinat.permutation.Permutation.multi_major_index[0]>", line 1, in <module>
        Permutation([Integer(5), Integer(6), Integer(2), Integer(1), Integer(3), Integer(7), Integer(4)]).multi_major_index(Composition([Integer(3), Integer(2), Integer(2)]))
      File "/__w/sagetrac-mirror/sagetrac-mirror/src/sage/combinat/permutation.py", line 3394, in multi_major_index
        for i, qi in enumerate(q):
    NameError: name 'q' is not defined

[fchapoton]

comment:4

also please write the full real names in the "Authors" field here above.

[slel]

Changed keywords from permutations, major index to permutations, major index, days114/club

[slel]

comment:5

This ticket is being worked on as part of the
Chennai Sage Club.

Reviewer commits are coming up next week.

Regarding names, these are the full names. (I had the same doubt and asked).

---

Further reading on names:

• https://www.kalzumeus.com/2010/06/17/falsehoods-programmers-believe-about-names/
• https://shinesolutions.com/2018/01/08/falsehoods-programmers-believe-about-names-with-examples/
• https://en.wikipedia.org/wiki/Indian_name#Tamil
• https://www.w3.org/International/wiki/Personal_names
• https://www.w3.org/International/questions/qa-personal-names

In particular, that last page hints single letter names exist,
and are not always initials.

[sagetrac-git]

Changed commit from 2cb5411 to 5e55c77

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

5e55c77

Speed up multimajor index

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

53cc12d

Add examples for multimajor index

[sagetrac-git]

Changed commit from 5e55c77 to 53cc12d

[aritra-bhattacharya-0]

Changed branch from u/gh-25shriya/34373 to public/34373

[aritra-bhattacharya-0]

Changed commit from 53cc12d to 1a468ca

[aritra-bhattacharya-0]

Changed author from Amrutha P, Shriya M, Divya Aggarwal to Amrutha P, Shriya M, Divya Aggarwal, Aritra Bhattacharya

[aritra-bhattacharya-0]

New commits:

1a468ca

Improve wording

[fchapoton]

comment:10

the meaning of :meth:`size` in the INPUT is not clear

the raise ValueError code line should be tested by a doctest inside TESTS::

[sagetrac-git]

Changed commit from 1a468ca to 9a93d1d

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

9a93d1d

Add doctest for multimajor index

[saraedum]

Reviewer: Amrutha P, Aritra Bhattacharya, Julian Rüth, Samuel Lelièvre

[vbraun]

Changed branch from public/34373 to 9a93d1d