- FindStat

edit this statistic or download as text // json

Identifier

St001598: Plane partitions ⟶ ℤ

Values

[[1]] => 0

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

[[2]] => 1

[[1,1]] => 1

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

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

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

[[3]] => 2

[[2,1]] => 1

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

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

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

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

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

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

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

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

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

[[4]] => 3

[[3,1]] => 2

[[2,2]] => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[5]] => 4

[[4,1]] => 3

[[3,2]] => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[6]] => 5

[[5,1]] => 4

[[4,2]] => 3

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

[[3,3]] => 3

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 1123 entries. <<<

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

Description

The maximal distance of a cell from the origin.
Put differently, this is the maximal sum of coordinates of a cell.
This statistic is undefined for the empty plane partition.

Code

def statistic(PP):
    return max(sum(c) for c in PP.cells())

Created

Sep 26, 2020 at 00:04 by Martin Rubey

Updated

Sep 26, 2020 at 00:04 by Martin Rubey