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Following the definition in https://arxiv.org/pdf/1508.05446.pdf 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?

Following the definition in https://arxiv.org/pdf/1508.05446.pdf 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?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

Following the definition in https://arxiv.org/pdf/1508.05446.pdf 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? 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.