- FindStat

edit this map or download as text // json

Identifier

Mp00311: Plane partitions —to partition⟶ Integer partitions

Images

[[1]] => [1]

[[1],[1]] => [1,1]

[[2]] => [2]

[[1,1]] => [2]

[[1],[1],[1]] => [1,1,1]

[[2],[1]] => [2,1]

[[1,1],[1]] => [2,1]

[[3]] => [3]

[[2,1]] => [3]

[[1,1,1]] => [3]

[[1],[1],[1],[1]] => [1,1,1,1]

[[2],[1],[1]] => [2,1,1]

[[2],[2]] => [2,2]

[[1,1],[1],[1]] => [2,1,1]

[[1,1],[1,1]] => [2,2]

[[3],[1]] => [3,1]

[[2,1],[1]] => [3,1]

[[1,1,1],[1]] => [3,1]

[[4]] => [4]

[[3,1]] => [4]

[[2,2]] => [4]

[[2,1,1]] => [4]

[[1,1,1,1]] => [4]

[[1],[1],[1],[1],[1]] => [1,1,1,1,1]

[[2],[1],[1],[1]] => [2,1,1,1]

[[2],[2],[1]] => [2,2,1]

[[1,1],[1],[1],[1]] => [2,1,1,1]

[[1,1],[1,1],[1]] => [2,2,1]

[[3],[1],[1]] => [3,1,1]

[[3],[2]] => [3,2]

[[2,1],[1],[1]] => [3,1,1]

[[2,1],[2]] => [3,2]

[[2,1],[1,1]] => [3,2]

[[1,1,1],[1],[1]] => [3,1,1]

[[1,1,1],[1,1]] => [3,2]

[[4],[1]] => [4,1]

[[3,1],[1]] => [4,1]

[[2,2],[1]] => [4,1]

[[2,1,1],[1]] => [4,1]

[[1,1,1,1],[1]] => [4,1]

[[5]] => [5]

[[4,1]] => [5]

[[3,2]] => [5]

[[3,1,1]] => [5]

[[2,2,1]] => [5]

[[2,1,1,1]] => [5]

[[1,1,1,1,1]] => [5]

[[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1]

[[2],[1],[1],[1],[1]] => [2,1,1,1,1]

[[2],[2],[1],[1]] => [2,2,1,1]

[[2],[2],[2]] => [2,2,2]

[[1,1],[1],[1],[1],[1]] => [2,1,1,1,1]

[[1,1],[1,1],[1],[1]] => [2,2,1,1]

[[1,1],[1,1],[1,1]] => [2,2,2]

[[3],[1],[1],[1]] => [3,1,1,1]

[[3],[2],[1]] => [3,2,1]

[[3],[3]] => [3,3]

[[2,1],[1],[1],[1]] => [3,1,1,1]

[[2,1],[2],[1]] => [3,2,1]

[[2,1],[1,1],[1]] => [3,2,1]

[[2,1],[2,1]] => [3,3]

[[1,1,1],[1],[1],[1]] => [3,1,1,1]

[[1,1,1],[1,1],[1]] => [3,2,1]

[[1,1,1],[1,1,1]] => [3,3]

[[4],[1],[1]] => [4,1,1]

[[4],[2]] => [4,2]

[[3,1],[1],[1]] => [4,1,1]

[[3,1],[2]] => [4,2]

[[3,1],[1,1]] => [4,2]

[[2,2],[1],[1]] => [4,1,1]

[[2,2],[2]] => [4,2]

[[2,2],[1,1]] => [4,2]

[[2,1,1],[1],[1]] => [4,1,1]

[[2,1,1],[2]] => [4,2]

[[2,1,1],[1,1]] => [4,2]

[[1,1,1,1],[1],[1]] => [4,1,1]

[[1,1,1,1],[1,1]] => [4,2]

[[5],[1]] => [5,1]

[[4,1],[1]] => [5,1]

[[3,2],[1]] => [5,1]

[[3,1,1],[1]] => [5,1]

[[2,2,1],[1]] => [5,1]

[[2,1,1,1],[1]] => [5,1]

[[1,1,1,1,1],[1]] => [5,1]

[[6]] => [6]

[[5,1]] => [6]

[[4,2]] => [6]

[[4,1,1]] => [6]

[[3,3]] => [6]

[[3,2,1]] => [6]

[[3,1,1,1]] => [6]

[[2,2,2]] => [6]

[[2,2,1,1]] => [6]

[[2,1,1,1,1]] => [6]

[[1,1,1,1,1,1]] => [6]

[[1],[1],[1],[1],[1],[1],[1]] => [1,1,1,1,1,1,1]

[[2],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1]

[[2],[2],[1],[1],[1]] => [2,2,1,1,1]

[[2],[2],[2],[1]] => [2,2,2,1]

[[1,1],[1],[1],[1],[1],[1]] => [2,1,1,1,1,1]

[[1,1],[1,1],[1],[1],[1]] => [2,2,1,1,1]

>>> Load all 1123 entries. <<<

click to show experimental identities (only identities of compositions of up to three maps are shown)

Description

The underlying integer partition of a plane partition.
This is the partition whose parts are the sums of the individual rows of the plane partition.

Properties

graded

Sage code

def mapping(p):
    return Partition(sum(row) for row in p)

Weight

Created

Aug 28, 2023 at 10:00 by Martin Rubey

Updated

Aug 28, 2023 at 10:00 by Martin Rubey