Plane Partitions¶
AUTHORS:
- Jang Soo Kim (2016): Initial implementation
- Jessica Striker (2016): Added additional methods
-
sage.combinat.plane_partition.
PlanePartition
¶ A plane partition.
A plane partition is a stack of cubes in the positive orthant.
INPUT:
PP
– a list of lists which represents a tableaubox_size
– (optional) a list[A, B, C]
of 3 positive integers, whereA
,B
,C
are the lengths of the box in the \(x\)-axis, \(y\)-axis, \(z\)-axis, respectively; if this is not given, it is determined by the smallest box boundingPP
OUTPUT:
The plane partition whose tableau representation is
PP
.EXAMPLES:
sage: PP = PlanePartition([[4,3,3,1],[2,1,1],[1,1]]) sage: PP Plane partition [[4, 3, 3, 1], [2, 1, 1], [1, 1]]
-
sage.combinat.plane_partition.
PlanePartitions
¶ All plane partitions inside a rectangular box of given side lengths.
INPUT:
box_size
– a triple of positive integers indicating the size of the box containing the plane partition
EXAMPLES:
This will create an instance to manipulate the plane partitions in a \(4 \times 3 \times 2\) box:
sage: P = PlanePartitions((4,3,2)) sage: P Plane partitions inside a 4 x 3 x 2 box sage: P.cardinality() 490
See also