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 tableau
  • box_size – (optional) a list [A, B, C] of 3 positive integers, where A, 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 bounding PP

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

PlanePartition