edit this statistic or download as text // json
Identifier
Values
[1] => 1
[2] => 1
[1,1] => 1
[3] => 1
[2,1] => 2
[1,1,1] => 1
[4] => 1
[3,1] => 3
[2,2] => 1
[2,1,1] => 3
[1,1,1,1] => 1
[5] => 1
[4,1] => 4
[3,2] => 2
[3,1,1] => 6
[2,2,1] => 3
[2,1,1,1] => 4
[1,1,1,1,1] => 1
[6] => 1
[5,1] => 5
[4,2] => 3
[4,1,1] => 10
[3,3] => 1
[3,2,1] => 7
[3,1,1,1] => 10
[2,2,2] => 1
[2,2,1,1] => 6
[2,1,1,1,1] => 5
[1,1,1,1,1,1] => 1
[7] => 1
[6,1] => 6
[5,2] => 4
[5,1,1] => 15
[4,3] => 2
[4,2,1] => 12
[4,1,1,1] => 20
[3,3,1] => 6
[3,2,2] => 3
[3,2,1,1] => 16
[3,1,1,1,1] => 15
[2,2,2,1] => 4
[2,2,1,1,1] => 10
[2,1,1,1,1,1] => 6
[1,1,1,1,1,1,1] => 1
[8] => 1
[7,1] => 7
[6,2] => 5
[6,1,1] => 21
[5,3] => 3
[5,2,1] => 18
[5,1,1,1] => 35
[4,4] => 1
[4,3,1] => 12
[4,2,2] => 6
[4,2,1,1] => 31
[4,1,1,1,1] => 35
[3,3,2] => 3
[3,3,1,1] => 19
[3,2,2,1] => 13
[3,2,1,1,1] => 30
[3,1,1,1,1,1] => 21
[2,2,2,2] => 1
[2,2,2,1,1] => 10
[2,2,1,1,1,1] => 15
[2,1,1,1,1,1,1] => 7
[1,1,1,1,1,1,1,1] => 1
[9] => 1
[8,1] => 8
[7,2] => 6
[7,1,1] => 28
[6,3] => 4
[6,2,1] => 25
[6,1,1,1] => 56
[5,4] => 2
[5,3,1] => 19
[5,2,2] => 10
[5,2,1,1] => 52
[5,1,1,1,1] => 70
[4,4,1] => 10
[4,3,2] => 7
[4,3,1,1] => 40
[4,2,2,1] => 28
[4,2,1,1,1] => 65
[4,1,1,1,1,1] => 56
[3,3,3] => 1
[3,3,2,1] => 16
[3,3,1,1,1] => 45
[3,2,2,2] => 4
[3,2,2,1,1] => 35
[3,2,1,1,1,1] => 50
[3,1,1,1,1,1,1] => 28
[2,2,2,2,1] => 5
[2,2,2,1,1,1] => 20
[2,2,1,1,1,1,1] => 21
[2,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,1,1,1] => 1
[10] => 1
[9,1] => 9
[8,2] => 7
[8,1,1] => 36
[7,3] => 5
>>> Load all 400 entries. <<<
[7,2,1] => 33
[7,1,1,1] => 84
[6,4] => 3
[6,3,1] => 27
[6,2,2] => 15
[6,2,1,1] => 80
[6,1,1,1,1] => 126
[5,5] => 1
[5,4,1] => 18
[5,3,2] => 12
[5,3,1,1] => 68
[5,2,2,1] => 50
[5,2,1,1,1] => 121
[5,1,1,1,1,1] => 126
[4,4,2] => 6
[4,4,1,1] => 44
[4,3,3] => 3
[4,3,2,1] => 38
[4,3,1,1,1] => 101
[4,2,2,2] => 10
[4,2,2,1,1] => 81
[4,2,1,1,1,1] => 120
[4,1,1,1,1,1,1] => 84
[3,3,3,1] => 10
[3,3,2,2] => 6
[3,3,2,1,1] => 51
[3,3,1,1,1,1] => 90
[3,2,2,2,1] => 21
[3,2,2,1,1,1] => 75
[3,2,1,1,1,1,1] => 77
[3,1,1,1,1,1,1,1] => 36
[2,2,2,2,2] => 1
[2,2,2,2,1,1] => 15
[2,2,2,1,1,1,1] => 35
[2,2,1,1,1,1,1,1] => 28
[2,1,1,1,1,1,1,1,1] => 9
[1,1,1,1,1,1,1,1,1,1] => 1
[11] => 1
[10,1] => 10
[9,2] => 8
[9,1,1] => 45
[8,3] => 6
[8,2,1] => 42
[8,1,1,1] => 120
[7,4] => 4
[7,3,1] => 36
[7,2,2] => 21
[7,2,1,1] => 116
[7,1,1,1,1] => 210
[6,5] => 2
[6,4,1] => 27
[6,3,2] => 18
[6,3,1,1] => 104
[6,2,2,1] => 80
[6,2,1,1,1] => 205
[6,1,1,1,1,1] => 252
[5,5,1] => 15
[5,4,2] => 12
[5,4,1,1] => 80
[5,3,3] => 6
[5,3,2,1] => 68
[5,3,1,1,1] => 185
[5,2,2,2] => 20
[5,2,2,1,1] => 155
[5,2,1,1,1,1] => 246
[5,1,1,1,1,1,1] => 210
[4,4,3] => 3
[4,4,2,1] => 40
[4,4,1,1,1] => 135
[4,3,3,1] => 28
[4,3,2,2] => 16
[4,3,2,1,1] => 125
[4,3,1,1,1,1] => 216
[4,2,2,2,1] => 55
[4,2,2,1,1,1] => 186
[4,2,1,1,1,1,1] => 203
[4,1,1,1,1,1,1,1] => 120
[3,3,3,2] => 4
[3,3,3,1,1] => 45
[3,3,2,2,1] => 35
[3,3,2,1,1,1] => 126
[3,3,1,1,1,1,1] => 161
[3,2,2,2,2] => 5
[3,2,2,2,1,1] => 66
[3,2,2,1,1,1,1] => 140
[3,2,1,1,1,1,1,1] => 112
[3,1,1,1,1,1,1,1,1] => 45
[2,2,2,2,2,1] => 6
[2,2,2,2,1,1,1] => 35
[2,2,2,1,1,1,1,1] => 56
[2,2,1,1,1,1,1,1,1] => 36
[2,1,1,1,1,1,1,1,1,1] => 10
[1,1,1,1,1,1,1,1,1,1,1] => 1
[12] => 1
[11,1] => 11
[10,2] => 9
[10,1,1] => 55
[9,3] => 7
[9,2,1] => 52
[9,1,1,1] => 165
[8,4] => 5
[8,3,1] => 46
[8,2,2] => 28
[8,2,1,1] => 161
[8,1,1,1,1] => 330
[7,5] => 3
[7,4,1] => 37
[7,3,2] => 25
[7,3,1,1] => 149
[7,2,2,1] => 119
[7,2,1,1,1] => 325
[7,1,1,1,1,1] => 462
[6,6] => 1
[6,5,1] => 25
[6,4,2] => 19
[6,4,1,1] => 125
[6,3,3] => 10
[6,3,2,1] => 107
[6,3,1,1,1] => 305
[6,2,2,2] => 35
[6,2,2,1,1] => 265
[6,2,1,1,1,1] => 456
[6,1,1,1,1,1,1] => 462
[5,5,2] => 10
[5,5,1,1] => 85
[5,4,3] => 7
[5,4,2,1] => 79
[5,4,1,1,1] => 255
[5,3,3,1] => 55
[5,3,2,2] => 31
[5,3,2,1,1] => 235
[5,3,1,1,1,1] => 426
[5,2,2,2,1] => 115
[5,2,2,1,1,1] => 381
[5,2,1,1,1,1,1] => 455
[5,1,1,1,1,1,1,1] => 330
[4,4,4] => 1
[4,4,3,1] => 31
[4,4,2,2] => 19
[4,4,2,1,1] => 155
[4,4,1,1,1,1] => 336
[4,3,3,2] => 13
[4,3,3,1,1] => 125
[4,3,2,2,1] => 95
[4,3,2,1,1,1] => 321
[4,3,1,1,1,1,1] => 413
[4,2,2,2,2] => 15
[4,2,2,2,1,1] => 181
[4,2,2,1,1,1,1] => 371
[4,2,1,1,1,1,1,1] => 322
[4,1,1,1,1,1,1,1,1] => 165
[3,3,3,3] => 1
[3,3,3,2,1] => 30
[3,3,3,1,1,1] => 141
[3,3,2,2,2] => 10
[3,3,2,2,1,1] => 121
[3,3,2,1,1,1,1] => 266
[3,3,1,1,1,1,1,1] => 266
[3,2,2,2,2,1] => 31
[3,2,2,2,1,1,1] => 161
[3,2,2,1,1,1,1,1] => 238
[3,2,1,1,1,1,1,1,1] => 156
[3,1,1,1,1,1,1,1,1,1] => 55
[2,2,2,2,2,2] => 1
[2,2,2,2,2,1,1] => 21
[2,2,2,2,1,1,1,1] => 70
[2,2,2,1,1,1,1,1,1] => 84
[2,2,1,1,1,1,1,1,1,1] => 45
[2,1,1,1,1,1,1,1,1,1,1] => 11
[1,1,1,1,1,1,1,1,1,1,1,1] => 1
[13] => 1
[12,1] => 12
[11,2] => 10
[11,1,1] => 66
[10,3] => 8
[10,2,1] => 63
[10,1,1,1] => 220
[9,4] => 6
[9,3,1] => 57
[9,2,2] => 36
[9,2,1,1] => 216
[9,1,1,1,1] => 495
[8,5] => 4
[8,4,1] => 48
[8,3,2] => 33
[8,3,1,1] => 204
[8,2,2,1] => 168
[8,2,1,1,1] => 490
[8,1,1,1,1,1] => 792
[7,6] => 2
[7,5,1] => 36
[7,4,2] => 27
[7,4,1,1] => 180
[7,3,3] => 15
[7,3,2,1] => 156
[7,3,1,1,1] => 470
[7,2,2,2] => 56
[7,2,2,1,1] => 420
[7,2,1,1,1,1] => 786
[7,1,1,1,1,1,1] => 924
[6,6,1] => 21
[6,5,2] => 18
[6,5,1,1] => 140
[6,4,3] => 12
[6,4,2,1] => 128
[6,4,1,1,1] => 420
[6,3,3,1] => 92
[6,3,2,2] => 52
[6,3,2,1,1] => 390
[6,3,1,1,1,1] => 756
[6,2,2,2,1] => 210
[6,2,2,1,1,1] => 696
[6,2,1,1,1,1,1] => 917
[6,1,1,1,1,1,1,1] => 792
[5,5,3] => 6
[5,5,2,1] => 80
[5,5,1,1,1] => 320
[5,4,4] => 3
[5,4,3,1] => 68
[5,4,2,2] => 40
[5,4,2,1,1] => 310
[5,4,1,1,1,1] => 666
[5,3,3,2] => 28
[5,3,3,1,1] => 250
[5,3,2,2,1] => 190
[5,3,2,1,1,1] => 636
[5,3,1,1,1,1,1] => 875
[5,2,2,2,2] => 35
[5,2,2,2,1,1] => 396
[5,2,2,1,1,1,1] => 812
[5,2,1,1,1,1,1,1] => 784
[5,1,1,1,1,1,1,1,1] => 495
[4,4,4,1] => 20
[4,4,3,2] => 16
[4,4,3,1,1] => 155
[4,4,2,2,1] => 125
[4,4,2,1,1,1] => 456
[4,4,1,1,1,1,1] => 728
[4,3,3,3] => 4
[4,3,3,2,1] => 95
[4,3,3,1,1,1] => 396
[4,3,2,2,2] => 30
[4,3,2,2,1,1] => 336
[4,3,2,1,1,1,1] => 707
[4,3,1,1,1,1,1,1] => 728
[4,2,2,2,2,1] => 96
[4,2,2,2,1,1,1] => 462
[4,2,2,1,1,1,1,1] => 672
[4,2,1,1,1,1,1,1,1] => 486
[4,1,1,1,1,1,1,1,1,1] => 220
[3,3,3,3,1] => 15
[3,3,3,2,2] => 10
[3,3,3,2,1,1] => 126
[3,3,3,1,1,1,1] => 357
[3,3,2,2,2,1] => 66
[3,3,2,2,1,1,1] => 322
[3,3,2,1,1,1,1,1] => 504
[3,3,1,1,1,1,1,1,1] => 414
[3,2,2,2,2,2] => 6
[3,2,2,2,2,1,1] => 112
[3,2,2,2,1,1,1,1] => 336
[3,2,2,1,1,1,1,1,1] => 378
[3,2,1,1,1,1,1,1,1,1] => 210
[3,1,1,1,1,1,1,1,1,1,1] => 66
[2,2,2,2,2,2,1] => 7
[2,2,2,2,2,1,1,1] => 56
[2,2,2,2,1,1,1,1,1] => 126
[2,2,2,1,1,1,1,1,1,1] => 120
[2,2,1,1,1,1,1,1,1,1,1] => 55
[2,1,1,1,1,1,1,1,1,1,1,1] => 12
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[14] => 1
[13,1] => 13
[12,2] => 11
[12,1,1] => 78
[11,3] => 9
[11,2,1] => 75
[11,1,1,1] => 286
[10,4] => 7
[10,3,1] => 69
[10,2,2] => 45
[10,2,1,1] => 282
[10,1,1,1,1] => 715
[9,5] => 5
[9,4,1] => 60
[9,3,2] => 42
[9,3,1,1] => 270
[9,2,2,1] => 228
[9,2,1,1,1] => 710
[9,1,1,1,1,1] => 1287
[8,6] => 3
[8,5,1] => 48
[8,4,2] => 36
[8,4,1,1] => 246
[8,3,3] => 21
[8,3,2,1] => 216
[8,3,1,1,1] => 690
[8,2,2,2] => 84
[8,2,2,1,1] => 630
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 number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition.
For example, there are eight tableaux of shape $[3,2,1]$ with maximal entry $3$, but two of them have the same weight.
References
[1] (bad identifier) MathOverflow:450294
Code
def statistic(la):
    s = SymmetricFunctions(ZZ).s()
    return len(list(s(la).expand(len(la))))
Created
Jul 06, 2023 at 19:05 by Martin Rubey
Updated
Jul 06, 2023 at 19:05 by Martin Rubey