Wrong gyration orbit length

[kliem]

sage -t --long --random-seed=103314966111765381642554237852288942819 src/sage/combinat/alternating_sign_matrix.py
**********************************************************************
File "src/sage/combinat/alternating_sign_matrix.py", line 609, in sage.combinat.alternating_sign_matrix.?.gyration
Failed example:
    a == a0
Expected:
    True
Got:
    False
**********************************************************************
1 item had failures:
   1 of  17 in sage.combinat.alternating_sign_matrix.?.gyration
    [313 tests, 1 failure, 0.83 s]

The claim of the doctest is that the orbit length of gyration on AlternatingSignMatrices(5) is a divisor of 10, which appears to be incorrect:

sage: def test_orbit_length(n): 
....:     a0 = a = AlternatingSignMatrices(n).random_element()    
....:     for i in range(10000): 
....:         a = a.gyration() 
....:         if a == a0: 
....:             return i + 1 
....:                                                                                                                                 
sage: lcm(foo(5) for _ in range(1000))                                                                                                
20

CC: @videlec

Component: combinatorics

Keywords: alternative sign matrices, gyration

Author: Jonathan Kliem

Branch/Commit: 1d021c1

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/32132

[kliem]

New commits:

1d021c1

fix orbit lenght of gyration

[kliem]

Author: Jonathan Kliem

[kliem]

Commit: 1d021c1

[kliem]

Branch: public/32132

[fchapoton]

comment:2

but see table 3.1 on page 6 of

http://www-users.math.umn.edu/~reiner/REU/CloningerDavidowitz2007.pdf

[kliem]

comment:3

But this is exactly what the table states. The orbit can be of length 2,4,5,10. The lowest common multiple being 20.

Thanks for the pointer. I didn't know where to look for this. So this isn't a bug apparently.

[fchapoton]

comment:4

the data of this table can be confirmed using

sage: def ma(M): 
....:     return matrix(ZZ,5,5, 
....:     M._matrix, immutable=True) 
....:                                                                           
sage: dg=DiGraph([(ma(x),ma(x.gyration())) for x in A])                         
sage: set(dg.connected_components_sizes())                                      
{2, 4, 5, 10}

[fchapoton]

comment:5

ok, good to go

[fchapoton]

Reviewer: Frédéric Chapoton

[kliem]

comment:6

Thank you.

[vbraun]

Changed branch from public/32132 to 1d021c1