- FindStat

edit this statistic or download as text // json

Identifier

St001914: Integer partitions ⟶ ℤ

Values

[1] => 1

[2] => 2

[1,1] => 2

[3] => 2

[2,1] => 1

[1,1,1] => 3

[4] => 4

[3,1] => 3

[2,2] => 3

[2,1,1] => 3

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

[5] => 5

[4,1] => 4

[3,2] => 3

[3,1,1] => 3

[2,2,1] => 3

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

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

[6] => 4

[5,1] => 3

[4,2] => 2

[4,1,1] => 6

[3,3] => 5

[3,2,1] => 1

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

[2,2,2] => 4

[2,2,1,1] => 7

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

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

[7] => 7

[6,1] => 6

[5,2] => 5

[5,1,1] => 6

[4,3] => 5

[4,2,1] => 4

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

[3,3,1] => 4

[3,2,2] => 4

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

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

[2,2,2,1] => 7

[2,2,1,1,1] => 7

[2,1,1,1,1,1] => 7

[1,1,1,1,1,1,1] => 8

[8] => 8

[7,1] => 7

[6,2] => 6

[6,1,1] => 4

[5,3] => 3

[5,2,1] => 5

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

[4,4] => 5

[4,3,1] => 4

[4,2,2] => 2

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

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

[3,3,2] => 4

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

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

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

[3,1,1,1,1,1] => 7

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

[2,2,2,1,1] => 7

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

[2,1,1,1,1,1,1] => 8

[1,1,1,1,1,1,1,1] => 9

[9] => 9

[8,1] => 8

[7,2] => 7

[7,1,1] => 7

[6,3] => 6

[6,2,1] => 6

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

[5,4] => 5

[5,3,1] => 5

[5,2,2] => 5

[5,2,1,1] => 10

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

[4,4,1] => 9

[4,3,2] => 4

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

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

[4,2,1,1,1] => 6

[4,1,1,1,1,1] => 7

[3,3,3] => 8

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

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

[3,2,2,2] => 7

[3,2,2,1,1] => 11

[3,2,1,1,1,1] => 7

[3,1,1,1,1,1,1] => 8

[2,2,2,2,1] => 7

[2,2,2,1,1,1] => 7

[2,2,1,1,1,1,1] => 8

[2,1,1,1,1,1,1,1] => 9

[1,1,1,1,1,1,1,1,1] => 10

[10] => 7

[9,1] => 6

[8,2] => 5

[8,1,1] => 10

[7,3] => 9

>>> Load all 1200 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 size of the orbit of an integer partition in Bulgarian solitaire.
Bulgarian solitaire is the dynamical system where a move consists of removing the first column of the Ferrers diagram and inserting it as a row.
This statistic returns the number of partitions that can be obtained from the given partition.

Code

def statistic(la):
    def move(la):
        return Partition(sorted([p-1 for p in la] + [len(la)], reverse=True))
    return len(DiscreteDynamicalSystem(Partitions(la.size()), move).orbit(la))

Created

Aug 14, 2023 at 16:29 by Martin Rubey

Updated

Aug 14, 2023 at 16:29 by Martin Rubey