Identifier
Identifier
Values
[2] generating graphics... => 1
[1,1] generating graphics... => 1
[3] generating graphics... => 1
[2,1] generating graphics... => 4
[1,1,1] generating graphics... => 1
[4] generating graphics... => 1
[3,1] generating graphics... => 9
[2,2] generating graphics... => 4
[2,1,1] generating graphics... => 9
[1,1,1,1] generating graphics... => 1
[5] generating graphics... => 1
[4,1] generating graphics... => 16
[3,2] generating graphics... => 25
[3,1,1] generating graphics... => 36
[2,2,1] generating graphics... => 25
[2,1,1,1] generating graphics... => 16
[1,1,1,1,1] generating graphics... => 1
[6] generating graphics... => 1
[5,1] generating graphics... => 25
[4,2] generating graphics... => 81
[4,1,1] generating graphics... => 100
[3,3] generating graphics... => 25
[3,2,1] generating graphics... => 256
[3,1,1,1] generating graphics... => 100
[2,2,2] generating graphics... => 25
[2,2,1,1] generating graphics... => 81
[2,1,1,1,1] generating graphics... => 25
[1,1,1,1,1,1] generating graphics... => 1
[7] generating graphics... => 1
[6,1] generating graphics... => 36
[5,2] generating graphics... => 196
[5,1,1] generating graphics... => 225
[4,3] generating graphics... => 196
[4,2,1] generating graphics... => 1225
[4,1,1,1] generating graphics... => 400
[3,3,1] generating graphics... => 441
[3,2,2] generating graphics... => 441
[3,2,1,1] generating graphics... => 1225
[3,1,1,1,1] generating graphics... => 225
[2,2,2,1] generating graphics... => 196
[2,2,1,1,1] generating graphics... => 196
[2,1,1,1,1,1] generating graphics... => 36
[1,1,1,1,1,1,1] generating graphics... => 1
[8] generating graphics... => 1
[7,1] generating graphics... => 49
[6,2] generating graphics... => 400
[6,1,1] generating graphics... => 441
[5,3] generating graphics... => 784
[5,2,1] generating graphics... => 4096
[5,1,1,1] generating graphics... => 1225
[4,4] generating graphics... => 196
[4,3,1] generating graphics... => 4900
[4,2,2] generating graphics... => 3136
[4,2,1,1] generating graphics... => 8100
[4,1,1,1,1] generating graphics... => 1225
[3,3,2] generating graphics... => 1764
[3,3,1,1] generating graphics... => 3136
[3,2,2,1] generating graphics... => 4900
[3,2,1,1,1] generating graphics... => 4096
[3,1,1,1,1,1] generating graphics... => 441
[2,2,2,2] generating graphics... => 196
[2,2,2,1,1] generating graphics... => 784
[2,2,1,1,1,1] generating graphics... => 400
[2,1,1,1,1,1,1] generating graphics... => 49
[1,1,1,1,1,1,1,1] generating graphics... => 1
[9] generating graphics... => 1
[8,1] generating graphics... => 64
[7,2] generating graphics... => 729
[7,1,1] generating graphics... => 784
[6,3] generating graphics... => 2304
[6,2,1] generating graphics... => 11025
[6,1,1,1] generating graphics... => 3136
[5,4] generating graphics... => 1764
[5,3,1] generating graphics... => 26244
[5,2,2] generating graphics... => 14400
[5,2,1,1] generating graphics... => 35721
[5,1,1,1,1] generating graphics... => 4900
[4,4,1] generating graphics... => 7056
[4,3,2] generating graphics... => 28224
[4,3,1,1] generating graphics... => 46656
[4,2,2,1] generating graphics... => 46656
[4,2,1,1,1] generating graphics... => 35721
[4,1,1,1,1,1] generating graphics... => 3136
[3,3,3] generating graphics... => 1764
[3,3,2,1] generating graphics... => 28224
[3,3,1,1,1] generating graphics... => 14400
[3,2,2,2] generating graphics... => 7056
[3,2,2,1,1] generating graphics... => 26244
[3,2,1,1,1,1] generating graphics... => 11025
[3,1,1,1,1,1,1] generating graphics... => 784
[2,2,2,2,1] generating graphics... => 1764
[2,2,2,1,1,1] generating graphics... => 2304
[2,2,1,1,1,1,1] generating graphics... => 729
[2,1,1,1,1,1,1,1] generating graphics... => 64
[1,1,1,1,1,1,1,1,1] generating graphics... => 1
[10] generating graphics... => 1
[9,1] generating graphics... => 81
[8,2] generating graphics... => 1225
[8,1,1] generating graphics... => 1296
[7,3] generating graphics... => 5625
[7,2,1] generating graphics... => 25600
[7,1,1,1] generating graphics... => 7056
[6,4] generating graphics... => 8100
[6,3,1] generating graphics... => 99225
[6,2,2] generating graphics... => 50625
[6,2,1,1] generating graphics... => 122500
[6,1,1,1,1] generating graphics... => 15876
[5,5] generating graphics... => 1764
[5,4,1] generating graphics... => 82944
[5,3,2] generating graphics... => 202500
[5,3,1,1] generating graphics... => 321489
[5,2,2,1] generating graphics... => 275625
[5,2,1,1,1] generating graphics... => 200704
[5,1,1,1,1,1] generating graphics... => 15876
[4,4,2] generating graphics... => 63504
[4,4,1,1] generating graphics... => 90000
[4,3,3] generating graphics... => 44100
[4,3,2,1] generating graphics... => 589824
[4,3,1,1,1] generating graphics... => 275625
[4,2,2,2] generating graphics... => 90000
[4,2,2,1,1] generating graphics... => 321489
[4,2,1,1,1,1] generating graphics... => 122500
[4,1,1,1,1,1,1] generating graphics... => 7056
[3,3,3,1] generating graphics... => 44100
[3,3,2,2] generating graphics... => 63504
[3,3,2,1,1] generating graphics... => 202500
[3,3,1,1,1,1] generating graphics... => 50625
[3,2,2,2,1] generating graphics... => 82944
[3,2,2,1,1,1] generating graphics... => 99225
[3,2,1,1,1,1,1] generating graphics... => 25600
[3,1,1,1,1,1,1,1] generating graphics... => 1296
[2,2,2,2,2] generating graphics... => 1764
[2,2,2,2,1,1] generating graphics... => 8100
[2,2,2,1,1,1,1] generating graphics... => 5625
[2,2,1,1,1,1,1,1] generating graphics... => 1225
[2,1,1,1,1,1,1,1,1] generating graphics... => 81
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[11] generating graphics... => 1
[10,1] generating graphics... => 100
[9,2] generating graphics... => 1936
[9,1,1] generating graphics... => 2025
[8,3] generating graphics... => 12100
[8,2,1] generating graphics... => 53361
[8,1,1,1] generating graphics... => 14400
[7,4] generating graphics... => 27225
[7,3,1] generating graphics... => 302500
[7,2,2] generating graphics... => 148225
[7,2,1,1] generating graphics... => 352836
[7,1,1,1,1] generating graphics... => 44100
[6,5] generating graphics... => 17424
[6,4,1] generating graphics... => 480249
[6,3,2] generating graphics... => 980100
[6,3,1,1] generating graphics... => 1517824
[6,2,2,1] generating graphics... => 1210000
[6,2,1,1,1] generating graphics... => 853776
[6,1,1,1,1,1] generating graphics... => 63504
[5,5,1] generating graphics... => 108900
[5,4,2] generating graphics... => 980100
[5,4,1,1] generating graphics... => 1334025
[5,3,3] generating graphics... => 435600
[5,3,2,1] generating graphics... => 5336100
[5,3,1,1,1] generating graphics... => 2371600
[5,2,2,2] generating graphics... => 680625
[5,2,2,1,1] generating graphics... => 2371600
[5,2,1,1,1,1] generating graphics... => 853776
[5,1,1,1,1,1,1] generating graphics... => 44100
[4,4,3] generating graphics... => 213444
[4,4,2,1] generating graphics... => 1742400
[4,4,1,1,1] generating graphics... => 680625
[4,3,3,1] generating graphics... => 1411344
[4,3,2,2] generating graphics... => 1742400
[4,3,2,1,1] generating graphics... => 5336100
[4,3,1,1,1,1] generating graphics... => 1210000
[4,2,2,2,1] generating graphics... => 1334025
[4,2,2,1,1,1] generating graphics... => 1517824
[4,2,1,1,1,1,1] generating graphics... => 352836
[4,1,1,1,1,1,1,1] generating graphics... => 14400
[3,3,3,2] generating graphics... => 213444
[3,3,3,1,1] generating graphics... => 435600
[3,3,2,2,1] generating graphics... => 980100
[3,3,2,1,1,1] generating graphics... => 980100
[3,3,1,1,1,1,1] generating graphics... => 148225
[3,2,2,2,2] generating graphics... => 108900
[3,2,2,2,1,1] generating graphics... => 480249
[3,2,2,1,1,1,1] generating graphics... => 302500
[3,2,1,1,1,1,1,1] generating graphics... => 53361
[3,1,1,1,1,1,1,1,1] generating graphics... => 2025
[2,2,2,2,2,1] generating graphics... => 17424
[2,2,2,2,1,1,1] generating graphics... => 27225
[2,2,2,1,1,1,1,1] generating graphics... => 12100
[2,2,1,1,1,1,1,1,1] generating graphics... => 1936
[2,1,1,1,1,1,1,1,1,1] generating graphics... => 100
[1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[12] generating graphics... => 1
[11,1] generating graphics... => 121
[10,2] generating graphics... => 2916
[10,1,1] generating graphics... => 3025
[9,3] generating graphics... => 23716
[9,2,1] generating graphics... => 102400
[9,1,1,1] generating graphics... => 27225
[8,4] generating graphics... => 75625
[8,3,1] generating graphics... => 793881
[8,2,2] generating graphics... => 379456
[8,2,1,1] generating graphics... => 893025
[8,1,1,1,1] generating graphics... => 108900
[7,5] generating graphics... => 88209
[7,4,1] generating graphics... => 1982464
[7,3,2] generating graphics... => 3705625
[7,3,1,1] generating graphics... => 5645376
[7,2,2,1] generating graphics... => 4322241
[7,2,1,1,1] generating graphics... => 2985984
[7,1,1,1,1,1] generating graphics... => 213444
[6,6] generating graphics... => 17424
[6,5,1] generating graphics... => 1334025
[6,4,2] generating graphics... => 7144929
[6,4,1,1] generating graphics... => 9486400
[6,3,3] generating graphics... => 2722500
[6,3,2,1] generating graphics... => 31719424
[6,3,1,1,1] generating graphics... => 13660416
[6,2,2,2] generating graphics... => 3705625
[6,2,2,1,1] generating graphics... => 12702096
[6,2,1,1,1,1] generating graphics... => 4410000
[6,1,1,1,1,1,1] generating graphics... => 213444
[5,5,2] generating graphics... => 1742400
[5,5,1,1] generating graphics... => 2205225
[5,4,3] generating graphics... => 4460544
[5,4,2,1] generating graphics... => 33350625
[5,4,1,1,1] generating graphics... => 12390400
[5,3,3,1] generating graphics... => 17288964
[5,3,2,2] generating graphics... => 19847025
[5,3,2,1,1] generating graphics... => 59290000
[5,3,1,1,1,1] generating graphics... => 12702096
[5,2,2,2,1] generating graphics... => 12390400
[5,2,2,1,1,1] generating graphics... => 13660416
[5,2,1,1,1,1,1] generating graphics... => 2985984
[5,1,1,1,1,1,1,1] generating graphics... => 108900
[4,4,4] generating graphics... => 213444
[4,4,3,1] generating graphics... => 8820900
[4,4,2,2] generating graphics... => 6969600
[4,4,2,1,1] generating graphics... => 19847025
[4,4,1,1,1,1] generating graphics... => 3705625
[4,3,3,2] generating graphics... => 8820900
[4,3,3,1,1] generating graphics... => 17288964
[4,3,2,2,1] generating graphics... => 33350625
[4,3,2,1,1,1] generating graphics... => 31719424
[4,3,1,1,1,1,1] generating graphics... => 4322241
[4,2,2,2,2] generating graphics... => 2205225
[4,2,2,2,1,1] generating graphics... => 9486400
[4,2,2,1,1,1,1] generating graphics... => 5645376
[4,2,1,1,1,1,1,1] generating graphics... => 893025
[4,1,1,1,1,1,1,1,1] generating graphics... => 27225
[3,3,3,3] generating graphics... => 213444
[3,3,3,2,1] generating graphics... => 4460544
[3,3,3,1,1,1] generating graphics... => 2722500
[3,3,2,2,2] generating graphics... => 1742400
[3,3,2,2,1,1] generating graphics... => 7144929
[3,3,2,1,1,1,1] generating graphics... => 3705625
[3,3,1,1,1,1,1,1] generating graphics... => 379456
[3,2,2,2,2,1] generating graphics... => 1334025
[3,2,2,2,1,1,1] generating graphics... => 1982464
[3,2,2,1,1,1,1,1] generating graphics... => 793881
[3,2,1,1,1,1,1,1,1] generating graphics... => 102400
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 3025
[2,2,2,2,2,2] generating graphics... => 17424
[2,2,2,2,2,1,1] generating graphics... => 88209
[2,2,2,2,1,1,1,1] generating graphics... => 75625
[2,2,2,1,1,1,1,1,1] generating graphics... => 23716
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 2916
[2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 121
[1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
click to show generating function       
Description
The Plancherel distribution on integer partitions.
This is defined as the distribution induced by the RSK shape of the uniform distribution on permutations. In other words, this is the size of the preimage of the map 'Robinson-Schensted tableau shape' from permutations to integer partitions.
Equivalently, this is given by the square of the number of standard Young tableaux of the given shape.
Code
def statistic(L):
    return L.standard_tableaux().cardinality()^2
Created
Sep 15, 2015 at 08:40 by Martin Rubey
Updated
Jul 12, 2017 at 10:03 by Christian Stump