- FindStat

edit this statistic or download as text // json

Identifier

St000048: Integer partitions ⟶ ℤ

Values

[] => 1

[1] => 1

[2] => 1

[1,1] => 2

[3] => 1

[2,1] => 3

[1,1,1] => 6

[4] => 1

[3,1] => 4

[2,2] => 6

[2,1,1] => 12

[1,1,1,1] => 24

[5] => 1

[4,1] => 5

[3,2] => 10

[3,1,1] => 20

[2,2,1] => 30

[2,1,1,1] => 60

[1,1,1,1,1] => 120

[6] => 1

[5,1] => 6

[4,2] => 15

[4,1,1] => 30

[3,3] => 20

[3,2,1] => 60

[3,1,1,1] => 120

[2,2,2] => 90

[2,2,1,1] => 180

[2,1,1,1,1] => 360

[1,1,1,1,1,1] => 720

[7] => 1

[6,1] => 7

[5,2] => 21

[5,1,1] => 42

[4,3] => 35

[4,2,1] => 105

[4,1,1,1] => 210

[3,3,1] => 140

[3,2,2] => 210

[3,2,1,1] => 420

[3,1,1,1,1] => 840

[2,2,2,1] => 630

[2,2,1,1,1] => 1260

[2,1,1,1,1,1] => 2520

[1,1,1,1,1,1,1] => 5040

[8] => 1

[7,1] => 8

[6,2] => 28

[6,1,1] => 56

[5,3] => 56

[5,2,1] => 168

[5,1,1,1] => 336

[4,4] => 70

[4,3,1] => 280

[4,2,2] => 420

[4,2,1,1] => 840

[4,1,1,1,1] => 1680

[3,3,2] => 560

[3,3,1,1] => 1120

[3,2,2,1] => 1680

[3,2,1,1,1] => 3360

[3,1,1,1,1,1] => 6720

[2,2,2,2] => 2520

[2,2,2,1,1] => 5040

[2,2,1,1,1,1] => 10080

[2,1,1,1,1,1,1] => 20160

[1,1,1,1,1,1,1,1] => 40320

[9] => 1

[8,1] => 9

[7,2] => 36

[7,1,1] => 72

[6,3] => 84

[6,2,1] => 252

[6,1,1,1] => 504

[5,4] => 126

[5,3,1] => 504

[5,2,2] => 756

[5,2,1,1] => 1512

[5,1,1,1,1] => 3024

[4,4,1] => 630

[4,3,2] => 1260

[4,3,1,1] => 2520

[4,2,2,1] => 3780

[4,2,1,1,1] => 7560

[4,1,1,1,1,1] => 15120

[3,3,3] => 1680

[3,3,2,1] => 5040

[3,3,1,1,1] => 10080

[3,2,2,2] => 7560

[3,2,2,1,1] => 15120

[3,2,1,1,1,1] => 30240

[3,1,1,1,1,1,1] => 60480

[2,2,2,2,1] => 22680

[2,2,2,1,1,1] => 45360

[2,2,1,1,1,1,1] => 90720

[2,1,1,1,1,1,1,1] => 181440

[1,1,1,1,1,1,1,1,1] => 362880

[10] => 1

[9,1] => 10

[8,2] => 45

[8,1,1] => 90

>>> Load all 469 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 multinomial of the parts of a partition.
Given an integer partition $\lambda = [\lambda_1,\ldots,\lambda_k]$, this is the multinomial
$$\binom{|\lambda|}{\lambda_1,\ldots,\lambda_k}.$$
For any integer composition $\mu$ that is a rearrangement of $\lambda$, this is the number of ordered set partitions whose list of block sizes is $\mu$.

Code

def statistic(L):
    return multinomial(list(L))

Created

Mar 25, 2013 at 10:25 by Christian Stump

Updated

Oct 29, 2017 at 20:26 by Martin Rubey