a bijectionist's toolkit

[mantepse]

We provide a toolkit for the combinatorialist to help find functions ("statistics") s: A -> Z and bijections A -> B given sequences of finite sets A and B that satisfy various constraints.

Closes #33238

📝 Checklist

• I have made sure that the title is self-explanatory and the description concisely explains the PR.
• I have linked an issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation accordingly.

[tscrim]

Thanks. LGTM.

[tscrim]

Sorry, accidentally hit the wrong button.

[mantepse]

Thank you so much! This ticket means a lot to me!

[vbraun]

On 32-bit:

**********************************************************************
File "src/sage/combinat/bijectionist.py", line 1578, in sage.combinat.bijectionist.Bijectionist._forced_constant_blocks
Failed example:
    for p in bij.constant_blocks(): print(list(p))
Expected:
    [[2, 1, 3, 4], [1, 2, 4, 3], [1, 3, 2, 4], [4, 2, 3, 1]]
    [[3, 2, 1], [1, 3, 2], [2, 1, 3]]
    [[2, 4, 3, 1], [3, 2, 4, 1], [2, 3, 1, 4], [1, 3, 4, 2]]
    [[1, 4, 2, 3], [3, 1, 2, 4], [4, 2, 1, 3], [4, 1, 3, 2]]
    [[1, 4, 3, 2], [3, 2, 1, 4]]
    [[2, 1, 4, 3], [4, 3, 2, 1]]
    [[2, 4, 1, 3], [3, 4, 2, 1], [4, 3, 1, 2], [3, 1, 4, 2]]
Got:
    [[1, 2, 4, 3], [4, 2, 3, 1], [1, 3, 2, 4], [2, 1, 3, 4]]
    [[2, 1, 3], [3, 2, 1], [1, 3, 2]]
    [[1, 3, 4, 2], [2, 3, 1, 4], [3, 2, 4, 1], [2, 4, 3, 1]]
    [[3, 1, 2, 4], [4, 2, 1, 3], [4, 1, 3, 2], [1, 4, 2, 3]]
    [[3, 2, 1, 4], [1, 4, 3, 2]]
    [[2, 1, 4, 3], [4, 3, 2, 1]]
    [[3, 4, 2, 1], [2, 4, 1, 3], [4, 3, 1, 2], [3, 1, 4, 2]]
**********************************************************************
File "src/sage/combinat/bijectionist.py", line 1587, in sage.combinat.bijectionist.Bijectionist._forced_constant_blocks
Failed example:
    for p in bij.constant_blocks(optimal=True): sorted(p, key=len)
Expected:
    [[1], [1, 2], [1, 2, 3], [1, 2, 3, 4]]
    [[1, 3, 2],
     [2, 1, 3],
     [3, 2, 1],
     [2, 3, 4, 1],
     [1, 3, 4, 2],
     [2, 1, 3, 4],
     [1, 3, 2, 4],
     [2, 3, 1, 4],
     [1, 2, 4, 3],
     [3, 2, 4, 1],
     [2, 1, 4, 3],
     [2, 4, 3, 1],
     [4, 2, 3, 1],
     [4, 3, 2, 1],
     [1, 4, 3, 2],
     [3, 2, 1, 4]]
    [[1, 4, 2, 3],
     [4, 2, 1, 3],
     [2, 4, 1, 3],
     [4, 3, 1, 2],
     [4, 1, 3, 2],
     [3, 4, 2, 1],
     [3, 1, 2, 4],
     [3, 1, 4, 2]]
Got:
    [[1], [1, 2], [1, 2, 3], [1, 2, 3, 4]]
    [[3, 2, 1],
     [1, 3, 2],
     [2, 1, 3],
     [2, 1, 4, 3],
     [1, 3, 2, 4],
     [2, 4, 3, 1],
     [1, 3, 4, 2],
     [2, 3, 1, 4],
     [3, 2, 1, 4],
     [4, 2, 3, 1],
     [1, 4, 3, 2],
     [2, 1, 3, 4],
     [1, 2, 4, 3],
     [3, 2, 4, 1],
     [4, 3, 2, 1],
     [2, 3, 4, 1]]
    [[3, 1, 2, 4],
     [4, 1, 3, 2],
     [4, 3, 1, 2],
     [1, 4, 2, 3],
     [3, 4, 2, 1],
     [4, 2, 1, 3],
     [2, 4, 1, 3],
     [3, 1, 4, 2]]
**********************************************************************
1 item had failures:
   2 of  65 in sage.combinat.bijectionist.Bijectionist._forced_constant_blocks
    [579 tests, 2 failures, 69.84 s]
----------------------------------------------------------------------
sage -t --long --random-seed=0 src/sage/combinat/bijectionist.py  # 2 doctests failed
----------------------------------------------------------------------

[mantepse]

@vbraun, I hope this solved the issue, but I have no way to test on 32 bit, I am sorry about that.

[github-actions]

Documentation preview for this PR is ready! 🎉
Built with commit: a72bd65

[tscrim]

I also think this sorting should solve the issue.