How to get the Area of a Dyck path
Given a Dyck path π, the Area(π) is the set of boxes (i,j) such that i<j and (i,j) is under π.
How to get the area of a given Dyck path from some given DyckWord pi ?
1 Answer
One can get easily get cells under the path from to_area_sequence(). For example:
dw = DyckWord([1,1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0,0])
A = [ (j,i) for i,J in enumerate(dw.to_area_sequence()) for j in range(J) ]
assert len(A) == dw.area()
print(A)gives
[(0, 1), (0, 2), (1, 2), (0, 3), (1, 3), (0, 4), (1, 4), (2, 4), (0, 5), (1, 5), (2, 5), (3, 5), (0, 6), (1, 6), (0, 7), (1, 7), (2, 7), (0, 8), (1, 8)]Your Answer
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Asked: 0 years ago
Seen: 267 times
Last updated: Oct 09 '24
Somehow the latex is not rendering correctly, hope someone fixes it.
Didn't you read documentation? Or what is your concern? https://doc.sagemath.org/html/en/refe...
sage has area and area_sequence. area is the cardinality of the set Area. I want the set Area, not its cardinality.
What is the reason for downvote!
Sounds like a homework problem.