def to_perfect_matching(self):
r"""
Return the perfect matching associated to ``self``.
EXAMPLES::
sage: path_tableaux.DyckPath([0,1,2,1,2,1,0,1,0]).to_perfect_matching()
[(0, 5), (1, 2), (3, 4), (6, 7)]
TESTS::
sage: path_tableaux.DyckPath([1,2,1,2,1,0,1]).to_perfect_matching()
Traceback (most recent call last):
...
ValueError: [1, 2, 1, 2, 1, 0, 1] does not start at 0
"""
if self.is_skew():
raise ValueError("%s does not start at 0" % (str(self)))
w = self.to_word()
y = DyckWord(w)
pairs = set()
for i, a in enumerate(y):
c = y.associated_parenthesis(i)
if i < c:
pairs.add((i, c))
return PerfectMatching(pairs)
