Module kshape
source code
k-shapes
The k-interior of a partition is the subpartition whose
cells have hook sizes greater than k.
The k-boundary of a partition is the skew shape
given by the partition minus its k-interior.
The row (resp. column) shape of a partition
is the composition whose i-th part is the
number of cells in the i-th row (resp. column) of the
k-boundary. A partition is a k-shape if both its
row shape and column shape are partitions.
EXAMPLES:
Construct the 3-shape from the partition [4,3,2,2,1,1].
sage: x = KShape([4,3,2,2,1,1],3)
sage: x.outer_shape
[4, 3, 2, 2, 1, 1]
The k-interior is called inner_shape.
sage: x.inner_shape
[2, 2, 1, 1]
sage: x.row_shape
[2, 1, 1, 1, 1, 1]
sage: x.column_shape
[2, 2, 2, 1]
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my_flatten(lislis)
flattens by one level (joins a listlist into a list) |
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zero_extend(mu,
l)
Returns list mu unless its length is less than l, in which case zeroes are
appended to mu to make its length equal to l. |
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diagonal_index(x)
Given a cell x=[r,c], return its diagonal index c-r. |
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is_partition(p)
Is a list of integers a list of weakly decreasing nonnegative integers? |
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KShape(outer,
k)
Create a kshape object defined by its outer shape |
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Difference of two lists of integers assuing len(la) >= len(mu).
If len(la)>len(mu) then append zeroes to mu and then subtract.
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cells is a list of pairs of nonnegative integers.
p is a list of integers.
For each [r,c] in cells, increment the part r of p.
If r >= the current length of the list,
adjoin 1 to the list.
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