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-----------------------------------------------------------------------------
Statistic identifier: St000706
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The product of the factorials of the multiplicities of an integer partition.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(la):
return prod(factorial(p) for p in la.to_exp())
-----------------------------------------------------------------------------
Statistic values:
[2] => 1
[1,1] => 2
[3] => 1
[2,1] => 1
[1,1,1] => 6
[4] => 1
[3,1] => 1
[2,2] => 2
[2,1,1] => 2
[1,1,1,1] => 24
[5] => 1
[4,1] => 1
[3,2] => 1
[3,1,1] => 2
[2,2,1] => 2
[2,1,1,1] => 6
[1,1,1,1,1] => 120
[6] => 1
[5,1] => 1
[4,2] => 1
[4,1,1] => 2
[3,3] => 2
[3,2,1] => 1
[3,1,1,1] => 6
[2,2,2] => 6
[2,2,1,1] => 4
[2,1,1,1,1] => 24
[1,1,1,1,1,1] => 720
[7] => 1
[6,1] => 1
[5,2] => 1
[5,1,1] => 2
[4,3] => 1
[4,2,1] => 1
[4,1,1,1] => 6
[3,3,1] => 2
[3,2,2] => 2
[3,2,1,1] => 2
[3,1,1,1,1] => 24
[2,2,2,1] => 6
[2,2,1,1,1] => 12
[2,1,1,1,1,1] => 120
[1,1,1,1,1,1,1] => 5040
[8] => 1
[7,1] => 1
[6,2] => 1
[6,1,1] => 2
[5,3] => 1
[5,2,1] => 1
[5,1,1,1] => 6
[4,4] => 2
[4,3,1] => 1
[4,2,2] => 2
[4,2,1,1] => 2
[4,1,1,1,1] => 24
[3,3,2] => 2
[3,3,1,1] => 4
[3,2,2,1] => 2
[3,2,1,1,1] => 6
[3,1,1,1,1,1] => 120
[2,2,2,2] => 24
[2,2,2,1,1] => 12
[2,2,1,1,1,1] => 48
[2,1,1,1,1,1,1] => 720
[1,1,1,1,1,1,1,1] => 40320
[9] => 1
[8,1] => 1
[7,2] => 1
[7,1,1] => 2
[6,3] => 1
[6,2,1] => 1
[6,1,1,1] => 6
[5,4] => 1
[5,3,1] => 1
[5,2,2] => 2
[5,2,1,1] => 2
[5,1,1,1,1] => 24
[4,4,1] => 2
[4,3,2] => 1
[4,3,1,1] => 2
[4,2,2,1] => 2
[4,2,1,1,1] => 6
[4,1,1,1,1,1] => 120
[3,3,3] => 6
[3,3,2,1] => 2
[3,3,1,1,1] => 12
[3,2,2,2] => 6
[3,2,2,1,1] => 4
[3,2,1,1,1,1] => 24
[3,1,1,1,1,1,1] => 720
[2,2,2,2,1] => 24
[2,2,2,1,1,1] => 36
[2,2,1,1,1,1,1] => 240
[2,1,1,1,1,1,1,1] => 5040
[1,1,1,1,1,1,1,1,1] => 362880
[10] => 1
[9,1] => 1
[8,2] => 1
[8,1,1] => 2
[7,3] => 1
[7,2,1] => 1
[7,1,1,1] => 6
[6,4] => 1
[6,3,1] => 1
[6,2,2] => 2
[6,2,1,1] => 2
[6,1,1,1,1] => 24
[5,5] => 2
[5,4,1] => 1
[5,3,2] => 1
[5,3,1,1] => 2
[5,2,2,1] => 2
[5,2,1,1,1] => 6
[5,1,1,1,1,1] => 120
[4,4,2] => 2
[4,4,1,1] => 4
[4,3,3] => 2
[4,3,2,1] => 1
[4,3,1,1,1] => 6
[4,2,2,2] => 6
[4,2,2,1,1] => 4
[4,2,1,1,1,1] => 24
[4,1,1,1,1,1,1] => 720
[3,3,3,1] => 6
[3,3,2,2] => 4
[3,3,2,1,1] => 4
[3,3,1,1,1,1] => 48
[3,2,2,2,1] => 6
[3,2,2,1,1,1] => 12
[3,2,1,1,1,1,1] => 120
[3,1,1,1,1,1,1,1] => 5040
[2,2,2,2,2] => 120
[2,2,2,2,1,1] => 48
[2,2,2,1,1,1,1] => 144
[2,2,1,1,1,1,1,1] => 1440
[2,1,1,1,1,1,1,1,1] => 40320
[1,1,1,1,1,1,1,1,1,1] => 3628800
[11] => 1
[10,1] => 1
[9,2] => 1
[9,1,1] => 2
[8,3] => 1
[8,2,1] => 1
[8,1,1,1] => 6
[7,4] => 1
[7,3,1] => 1
[7,2,2] => 2
[7,2,1,1] => 2
[7,1,1,1,1] => 24
[6,5] => 1
[6,4,1] => 1
[6,3,2] => 1
[6,3,1,1] => 2
[6,2,2,1] => 2
[6,2,1,1,1] => 6
[6,1,1,1,1,1] => 120
[5,5,1] => 2
[5,4,2] => 1
[5,4,1,1] => 2
[5,3,3] => 2
[5,3,2,1] => 1
[5,3,1,1,1] => 6
[5,2,2,2] => 6
[5,2,2,1,1] => 4
[5,2,1,1,1,1] => 24
[5,1,1,1,1,1,1] => 720
[4,4,3] => 2
[4,4,2,1] => 2
[4,4,1,1,1] => 12
[4,3,3,1] => 2
[4,3,2,2] => 2
[4,3,2,1,1] => 2
[4,3,1,1,1,1] => 24
[4,2,2,2,1] => 6
[4,2,2,1,1,1] => 12
[4,2,1,1,1,1,1] => 120
[4,1,1,1,1,1,1,1] => 5040
[3,3,3,2] => 6
[3,3,3,1,1] => 12
[3,3,2,2,1] => 4
[3,3,2,1,1,1] => 12
[3,3,1,1,1,1,1] => 240
[3,2,2,2,2] => 24
[3,2,2,2,1,1] => 12
[3,2,2,1,1,1,1] => 48
[3,2,1,1,1,1,1,1] => 720
[3,1,1,1,1,1,1,1,1] => 40320
[2,2,2,2,2,1] => 120
[2,2,2,2,1,1,1] => 144
[2,2,2,1,1,1,1,1] => 720
[2,2,1,1,1,1,1,1,1] => 10080
[2,1,1,1,1,1,1,1,1,1] => 362880
[1,1,1,1,1,1,1,1,1,1,1] => 39916800
[12] => 1
[11,1] => 1
[10,2] => 1
[10,1,1] => 2
[9,3] => 1
[9,2,1] => 1
[9,1,1,1] => 6
[8,4] => 1
[8,3,1] => 1
[8,2,2] => 2
[8,2,1,1] => 2
[8,1,1,1,1] => 24
[7,5] => 1
[7,4,1] => 1
[7,3,2] => 1
[7,3,1,1] => 2
[7,2,2,1] => 2
[7,2,1,1,1] => 6
[7,1,1,1,1,1] => 120
[6,6] => 2
[6,5,1] => 1
[6,4,2] => 1
[6,4,1,1] => 2
[6,3,3] => 2
[6,3,2,1] => 1
[6,3,1,1,1] => 6
[6,2,2,2] => 6
[6,2,2,1,1] => 4
[6,2,1,1,1,1] => 24
[6,1,1,1,1,1,1] => 720
[5,5,2] => 2
[5,5,1,1] => 4
[5,4,3] => 1
[5,4,2,1] => 1
[5,4,1,1,1] => 6
[5,3,3,1] => 2
[5,3,2,2] => 2
[5,3,2,1,1] => 2
[5,3,1,1,1,1] => 24
[5,2,2,2,1] => 6
[5,2,2,1,1,1] => 12
[5,2,1,1,1,1,1] => 120
[5,1,1,1,1,1,1,1] => 5040
[4,4,4] => 6
[4,4,3,1] => 2
[4,4,2,2] => 4
[4,4,2,1,1] => 4
[4,4,1,1,1,1] => 48
[4,3,3,2] => 2
[4,3,3,1,1] => 4
[4,3,2,2,1] => 2
[4,3,2,1,1,1] => 6
[4,3,1,1,1,1,1] => 120
[4,2,2,2,2] => 24
[4,2,2,2,1,1] => 12
[4,2,2,1,1,1,1] => 48
[4,2,1,1,1,1,1,1] => 720
[4,1,1,1,1,1,1,1,1] => 40320
[3,3,3,3] => 24
[3,3,3,2,1] => 6
[3,3,3,1,1,1] => 36
[3,3,2,2,2] => 12
[3,3,2,2,1,1] => 8
[3,3,2,1,1,1,1] => 48
[3,3,1,1,1,1,1,1] => 1440
[3,2,2,2,2,1] => 24
[3,2,2,2,1,1,1] => 36
[3,2,2,1,1,1,1,1] => 240
[3,2,1,1,1,1,1,1,1] => 5040
[3,1,1,1,1,1,1,1,1,1] => 362880
[2,2,2,2,2,2] => 720
[2,2,2,2,2,1,1] => 240
[2,2,2,2,1,1,1,1] => 576
[2,2,2,1,1,1,1,1,1] => 4320
[2,2,1,1,1,1,1,1,1,1] => 80640
[2,1,1,1,1,1,1,1,1,1,1] => 3628800
[1,1,1,1,1,1,1,1,1,1,1,1] => 479001600
-----------------------------------------------------------------------------
Created: Mar 07, 2017 at 09:36 by Martin Rubey
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Last Updated: Mar 07, 2017 at 09:36 by Martin Rubey