Checking whether a poset is thin with Sage

asked 2023-03-19 14:56:30 +0200

klaaa gravatar image

updated 2023-03-20 14:14:03 +0200

Following the definition in after theorem 7.7 a finite graded poset (we can assume it is connected) is called thin if each interval [x,y] of rank 2 has cardinality 4. Is there a quick way to check with Sage whether a given graded poset is thin?

edit: Thanks to John Palmieri, who suggests to look at the code for is_slender() and modify it. Here is the code:

def is_slender(self, certificate=False):

for x in self:
        d = {}
        for y in self.upper_covers(x):
            for c in self.upper_covers(y):
                d[c] = d.get(c, 0) + 1
        for c, y in d.items():
            if y >= 3:
                if certificate:
                    return (False, (x, c))
                return False
    if certificate:
        return (True, None)
    return True

I do not fully understand it yet as Im not experienced with programming in SAGE but I will try to modify it a bit and see if Im succesful.

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The method .is_slenderis almost what you want: You could modify that to create a new method that does what you want.

John Palmieri gravatar imageJohn Palmieri ( 2023-03-19 20:50:14 +0200 )edit

Thank you for that comment. Do you know where I can find the program code for .is_slender to modify it?

klaaa gravatar imageklaaa ( 2023-03-20 01:49:13 +0200 )edit

If P is a poset, evaluate P.is_slender?? to view the source code. This should also print the name of the file containing that code. Alternatively, you can run search_def('is_slender') and it should print "combinat/posets/", which means that the code is in the file returned by os.path.join(SAGE_ROOT, 'src', 'sage', 'combinat', 'posets', '').

John Palmieri gravatar imageJohn Palmieri ( 2023-03-20 04:07:52 +0200 )edit

I don't know the code but you may just be able to replace if y >= 3: with if y >= 3 or y == 1:.

John Palmieri gravatar imageJohn Palmieri ( 2023-03-20 16:33:06 +0200 )edit

Thank you. I do some tests to see if this gives the right thing.

klaaa gravatar imageklaaa ( 2023-03-20 19:33:30 +0200 )edit