weak order of permutations broken

[tscrim]

From https://groups.google.com/forum/#!topic/sage-support/6kuvliWzi84:

sage: for w in Permutations(3):
....:     w, w.weak_covers()
....:
([1, 2, 3], [])
([1, 3, 2], [[1, 2, 3]])
([2, 1, 3], [[1, 2, 3]])
([2, 3, 1], [[3, 2, 1]])
([3, 1, 2], [[3, 2, 1]])
([3, 2, 1], [[3, 1, 2], [2, 3, 1]])

The fourth and fifth lines of the output are incorrect.
The correct values should be

([2, 3, 1], [[2, 1, 3]])
([3, 1, 2], [[1, 3, 2]])

This manifests also in creating the weak order poset:

sage: Permutations(3).weak_poset()
...
ValueError: Hasse diagram contains cycles

This is a left-vs-right issue and Permutation multiplication being a little strange with respect to that. We also remove the multiplication argument and convention effects from has_*_descent.

CC: @sagetrac-sage-combinat @nthiery @fchapoton @darijgr @sagetrac-jeremy-l-martin

Component: combinatorics

Keywords: Coxeter group

Author: Travis Scrimshaw

Branch/Commit: fa0450e

Reviewer: Frédéric Chapoton, Darij Grinberg

Issue created by migration from https://trac.sagemath.org/ticket/27467

[tscrim]

comment:2

The problem is the multiplication for a permutation seems to have the oppose effect (by default):

sage: W = Permutations(3)
sage: w = W([2,3,1])
sage: w.reduced_word()
[1, 2]
sage: w.descents(side='right')
[2]
sage: w.apply_simple_reflection_right(2)
[3, 2, 1]

So we need to override apply_simple_reflection_* for Permutation.

[tscrim]

Branch: public/combinat/fix_weak_order_permutations-27467

[tscrim]

Author: Travis Scrimshaw

[tscrim]

comment:3

So the only way forward that I could see to make this work is to gut out the multiplication option for has_*_descent. With this, I do not think anything for Coxeter combiantorics now uses the multiplication convention.

---

New commits:

2273223

Making apply_simple_reflection_* and has_*_descent not use the permutation multiplication convention.

[tscrim]

Commit: 2273223

[embray]

comment:5

Moving all blocker/critical issues from 8.7 to 8.8.

[tscrim]

comment:6

Can someone review this?

[sagetrac-git]

Changed commit from 2273223 to c54aef5

[sagetrac-git]

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

c822b3f	Merge branch 'public/combinat/fix_weak_order_permutations-27467' of git://trac.sagemath.org/sage into public/combinat/fix_weak_order_permutations-27467
c54aef5	Updating docstring based on comments by Darij.

[sagetrac-git]

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

295c517

Fixing Yokonuma-Hecke algebras.

[sagetrac-git]

Changed commit from c54aef5 to 295c517

[tscrim]

comment:9

Green patchbot.

[fchapoton]

comment:10

• deprecation should appear in doctests, no ?

• "switching the entries i and i+1" (remove "equal" ?) in the doc of apply_simple_reflection_right

• I am worried that this seems to be a source of incoherence.. But maybe the situation gets no worse than what it is right now ?

[sagetrac-git]

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

0af471b

Adding deprecation doctest and fixing docstring.

[sagetrac-git]

Changed commit from 295c517 to 0af471b

[tscrim]

comment:12

Replying to @fchapoton:

• deprecation should appear in doctests, no ?

Added.

• "switching the entries i and i+1" (remove "equal" ?) in the doc of apply_simple_reflection_right

Fixed.

• I am worried that this seems to be a source of incoherence.. But maybe the situation gets no worse than what it is right now ?

It is at least no worse than what it is currently, but I think this makes it more consistent overall. Plus it fixes a definite bug.

[fchapoton]

comment:13

ok, then.

One should suggest somewhere loudly to use SymmetricGroup(n) instead of Permutations(n) when doing Coxeter-related work.

[fchapoton]

Reviewer: Frédéric Chapoton

[tscrim]

comment:14

Replying to @fchapoton:

ok, then.

Thank you.

One should suggest somewhere loudly to use SymmetricGroup(n) instead of Permutations(n) when doing Coxeter-related work.

Also referencing CoxeterGroup or WeylGroup as well. Another ticket.

I am adding Darij as a reviewer since he gave me some comments on the ticket.

[tscrim]

Changed reviewer from Frédéric Chapoton to Frédéric Chapoton, Darij Grinberg

[vbraun]

comment:15

Possibly due to #27899, I'm getting

sage -t --warn-long 57.2 src/sage/combinat/dyck_word.py
**********************************************************************
File "src/sage/combinat/dyck_word.py", line 1997, in sage.combinat.dyck_word.DyckWord_complete.to_312_avoiding_permutation
Failed example:
    p = DyckWord([1,1,0,1,0,0,1,1,0,1,0,1,0,0]).to_312_avoiding_permutation(); p
Expected:
    [2, 3, 1, 5, 6, 7, 4]
Got:
    [3, 1, 2, 7, 4, 5, 6]
**********************************************************************
File "src/sage/combinat/dyck_word.py", line 2007, in sage.combinat.dyck_word.DyckWord_complete.to_312_avoiding_permutation
Failed example:
    all(pi.avoids([3,1,2]) for pi in PD)
Expected:
    True
Got:
    False
**********************************************************************
File "src/sage/combinat/dyck_word.py", line 2197, in sage.combinat.dyck_word.DyckWord_complete.to_permutation
Failed example:
    D.to_permutation(map="Bandlow-Killpatrick")
Expected:
    [3, 4, 2, 1]
Got:
    [4, 3, 1, 2]
**********************************************************************
2 items had failures:
   2 of   9 in sage.combinat.dyck_word.DyckWord_complete.to_312_avoiding_permutation
   1 of   7 in sage.combinat.dyck_word.DyckWord_complete.to_permutation
    [581 tests, 3 failures, 1.27 s]
----------------------------------------------------------------------
sage -t --warn-long 57.2 src/sage/combinat/dyck_word.py  # 3 doctests failed
----------------------------------------------------------------------

[fchapoton]

comment:16

Yes, probably correlated to this replacement in #27899 :

         n = self.semilength()
         area = self.to_area_sequence()
-        from sage.groups.perm_gps.permgroup_named import SymmetricGroup
-        pi = SymmetricGroup(n).one()
+        pi = Permutations(n).one()
         for j in range(n):
             for i in range(area[j]):
-                pi = pi.apply_simple_reflection(j-i)
-        return Permutation(~pi)
+                pi = pi.apply_simple_reflection(j - i)
+        return ~pi

[tscrim]

comment:17

I concur, and it should just be a matter of swapping the left/right convention (which I guess should just mean returning pi instead of ~pi). I can do this tomorrow.

[sagetrac-git]

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

25f8655

Merge branch 'public/combinat/fix_weak_order_permutations-27467' of git://trac.sagemath.org/sage into public/combinat/fix_weak_order_permutations-27467

[sagetrac-git]

Changed commit from 0af471b to 25f8655

[sagetrac-git]

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

fa0450e

Fixing left-right convention difference.

[sagetrac-git]

Changed commit from 25f8655 to fa0450e

[tscrim]

comment:20

Sorry, I got sidetracked from this and forgot to do this last week. This is now fixed (although unfortunately we might have missed the next release cutoff...). Volker, it would be really nice if this could slip in to 8.8 since this is a relatively big bug in the combinatorics code.

[fchapoton]

comment:21

set to positive again

[vbraun]

Changed branch from public/combinat/fix_weak_order_permutations-27467 to fa0450e