Identifier
Identifier
Values
[] generating graphics... => 1
[1] generating graphics... => 1
[2] generating graphics... => 1
[1,1] generating graphics... => 2
[3] generating graphics... => 1
[2,1] generating graphics... => 2
[1,1,1] generating graphics... => 4
[4] generating graphics... => 1
[3,1] generating graphics... => 2
[2,2] generating graphics... => 3
[2,1,1] generating graphics... => 5
[1,1,1,1] generating graphics... => 10
[5] generating graphics... => 1
[4,1] generating graphics... => 2
[3,2] generating graphics... => 3
[3,1,1] generating graphics... => 5
[2,2,1] generating graphics... => 7
[2,1,1,1] generating graphics... => 13
[1,1,1,1,1] generating graphics... => 26
[6] generating graphics... => 1
[5,1] generating graphics... => 2
[4,2] generating graphics... => 3
[4,1,1] generating graphics... => 5
[3,3] generating graphics... => 4
[3,2,1] generating graphics... => 8
[3,1,1,1] generating graphics... => 14
[2,2,2] generating graphics... => 11
[2,2,1,1] generating graphics... => 20
[2,1,1,1,1] generating graphics... => 38
[1,1,1,1,1,1] generating graphics... => 76
[7] generating graphics... => 1
[6,1] generating graphics... => 2
[5,2] generating graphics... => 3
[5,1,1] generating graphics... => 5
[4,3] generating graphics... => 4
[4,2,1] generating graphics... => 8
[4,1,1,1] generating graphics... => 14
[3,3,1] generating graphics... => 10
[3,2,2] generating graphics... => 13
[3,2,1,1] generating graphics... => 23
[3,1,1,1,1] generating graphics... => 42
[2,2,2,1] generating graphics... => 32
[2,2,1,1,1] generating graphics... => 60
[2,1,1,1,1,1] generating graphics... => 116
[1,1,1,1,1,1,1] generating graphics... => 232
[8] generating graphics... => 1
[7,1] generating graphics... => 2
[6,2] generating graphics... => 3
[6,1,1] generating graphics... => 5
[5,3] generating graphics... => 4
[5,2,1] generating graphics... => 8
[5,1,1,1] generating graphics... => 14
[4,4] generating graphics... => 5
[4,3,1] generating graphics... => 11
[4,2,2] generating graphics... => 14
[4,2,1,1] generating graphics... => 24
[4,1,1,1,1] generating graphics... => 43
[3,3,2] generating graphics... => 17
[3,3,1,1] generating graphics... => 30
[3,2,2,1] generating graphics... => 40
[3,2,1,1,1] generating graphics... => 73
[3,1,1,1,1,1] generating graphics... => 136
[2,2,2,2] generating graphics... => 56
[2,2,2,1,1] generating graphics... => 103
[2,2,1,1,1,1] generating graphics... => 196
[2,1,1,1,1,1,1] generating graphics... => 382
[1,1,1,1,1,1,1,1] generating graphics... => 764
[9] generating graphics... => 1
[8,1] generating graphics... => 2
[7,2] generating graphics... => 3
[7,1,1] generating graphics... => 5
[6,3] generating graphics... => 4
[6,2,1] generating graphics... => 8
[6,1,1,1] generating graphics... => 14
[5,4] generating graphics... => 5
[5,3,1] generating graphics... => 11
[5,2,2] generating graphics... => 14
[5,2,1,1] generating graphics... => 24
[5,1,1,1,1] generating graphics... => 43
[4,4,1] generating graphics... => 13
[4,3,2] generating graphics... => 19
[4,3,1,1] generating graphics... => 33
[4,2,2,1] generating graphics... => 43
[4,2,1,1,1] generating graphics... => 77
[4,1,1,1,1,1] generating graphics... => 141
[3,3,3] generating graphics... => 23
[3,3,2,1] generating graphics... => 53
[3,3,1,1,1] generating graphics... => 96
[3,2,2,2] generating graphics... => 72
[3,2,2,1,1] generating graphics... => 131
[3,2,1,1,1,1] generating graphics... => 244
[3,1,1,1,1,1,1] generating graphics... => 462
[2,2,2,2,1] generating graphics... => 184
[2,2,2,1,1,1] generating graphics... => 347
[2,2,1,1,1,1,1] generating graphics... => 668
[2,1,1,1,1,1,1,1] generating graphics... => 1310
[1,1,1,1,1,1,1,1,1] generating graphics... => 2620
[10] generating graphics... => 1
[9,1] generating graphics... => 2
[8,2] generating graphics... => 3
[8,1,1] generating graphics... => 5
[7,3] generating graphics... => 4
[7,2,1] generating graphics... => 8
[7,1,1,1] generating graphics... => 14
[6,4] generating graphics... => 5
[6,3,1] generating graphics... => 11
[6,2,2] generating graphics... => 14
[6,2,1,1] generating graphics... => 24
[6,1,1,1,1] generating graphics... => 43
[5,5] generating graphics... => 6
[5,4,1] generating graphics... => 14
[5,3,2] generating graphics... => 20
[5,3,1,1] generating graphics... => 34
[5,2,2,1] generating graphics... => 44
[5,2,1,1,1] generating graphics... => 78
[5,1,1,1,1,1] generating graphics... => 142
[4,4,2] generating graphics... => 23
[4,4,1,1] generating graphics... => 40
[4,3,3] generating graphics... => 27
[4,3,2,1] generating graphics... => 61
[4,3,1,1,1] generating graphics... => 109
[4,2,2,2] generating graphics... => 81
[4,2,2,1,1] generating graphics... => 145
[4,2,1,1,1,1] generating graphics... => 265
[4,1,1,1,1,1,1] generating graphics... => 492
[3,3,3,1] generating graphics... => 74
[3,3,2,2] generating graphics... => 100
[3,3,2,1,1] generating graphics... => 180
[3,3,1,1,1,1] generating graphics... => 332
[3,2,2,2,1] generating graphics... => 248
[3,2,2,1,1,1] generating graphics... => 460
[3,2,1,1,1,1,1] generating graphics... => 868
[3,1,1,1,1,1,1,1] generating graphics... => 1660
[2,2,2,2,2] generating graphics... => 348
[2,2,2,2,1,1] generating graphics... => 652
[2,2,2,1,1,1,1] generating graphics... => 1244
[2,2,1,1,1,1,1,1] generating graphics... => 2412
[2,1,1,1,1,1,1,1,1] generating graphics... => 4748
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 9496
[11] generating graphics... => 1
[10,1] generating graphics... => 2
[9,2] generating graphics... => 3
[9,1,1] generating graphics... => 5
[8,3] generating graphics... => 4
[8,2,1] generating graphics... => 8
[8,1,1,1] generating graphics... => 14
[7,4] generating graphics... => 5
[7,3,1] generating graphics... => 11
[7,2,2] generating graphics... => 14
[7,2,1,1] generating graphics... => 24
[7,1,1,1,1] generating graphics... => 43
[6,5] generating graphics... => 6
[6,4,1] generating graphics... => 14
[6,3,2] generating graphics... => 20
[6,3,1,1] generating graphics... => 34
[6,2,2,1] generating graphics... => 44
[6,2,1,1,1] generating graphics... => 78
[6,1,1,1,1,1] generating graphics... => 142
[5,5,1] generating graphics... => 16
[5,4,2] generating graphics... => 25
[5,4,1,1] generating graphics... => 43
[5,3,3] generating graphics... => 29
[5,3,2,1] generating graphics... => 64
[5,3,1,1,1] generating graphics... => 113
[5,2,2,2] generating graphics... => 84
[5,2,2,1,1] generating graphics... => 149
[5,2,1,1,1,1] generating graphics... => 270
[5,1,1,1,1,1,1] generating graphics... => 498
[4,4,3] generating graphics... => 33
[4,4,2,1] generating graphics... => 74
[4,4,1,1,1] generating graphics... => 132
[4,3,3,1] generating graphics... => 88
[4,3,2,2] generating graphics... => 117
[4,3,2,1,1] generating graphics... => 209
[4,3,1,1,1,1] generating graphics... => 381
[4,2,2,2,1] generating graphics... => 282
[4,2,2,1,1,1] generating graphics... => 516
[4,2,1,1,1,1,1] generating graphics... => 958
[4,1,1,1,1,1,1,1] generating graphics... => 1800
[3,3,3,2] generating graphics... => 143
[3,3,3,1,1] generating graphics... => 256
[3,3,2,2,1] generating graphics... => 350
[3,3,2,1,1,1] generating graphics... => 644
[3,3,1,1,1,1,1] generating graphics... => 1204
[3,2,2,2,2] generating graphics... => 484
[3,2,2,2,1,1] generating graphics... => 897
[3,2,2,1,1,1,1] generating graphics... => 1688
[3,2,1,1,1,1,1,1] generating graphics... => 3218
[3,1,1,1,1,1,1,1,1] generating graphics... => 6204
[2,2,2,2,2,1] generating graphics... => 1268
[2,2,2,2,1,1,1] generating graphics... => 2408
[2,2,2,1,1,1,1,1] generating graphics... => 4636
[2,2,1,1,1,1,1,1,1] generating graphics... => 9040
[2,1,1,1,1,1,1,1,1,1] generating graphics... => 17848
[1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 35696
[12] generating graphics... => 1
[11,1] generating graphics... => 2
[10,2] generating graphics... => 3
[10,1,1] generating graphics... => 5
[9,3] generating graphics... => 4
[9,2,1] generating graphics... => 8
[9,1,1,1] generating graphics... => 14
[8,4] generating graphics... => 5
[8,3,1] generating graphics... => 11
[8,2,2] generating graphics... => 14
[8,2,1,1] generating graphics... => 24
[8,1,1,1,1] generating graphics... => 43
[7,5] generating graphics... => 6
[7,4,1] generating graphics... => 14
[7,3,2] generating graphics... => 20
[7,3,1,1] generating graphics... => 34
[7,2,2,1] generating graphics... => 44
[7,2,1,1,1] generating graphics... => 78
[7,1,1,1,1,1] generating graphics... => 142
[6,6] generating graphics... => 7
[6,5,1] generating graphics... => 17
[6,4,2] generating graphics... => 26
[6,4,1,1] generating graphics... => 44
[6,3,3] generating graphics... => 30
[6,3,2,1] generating graphics... => 65
[6,3,1,1,1] generating graphics... => 114
[6,2,2,2] generating graphics... => 85
[6,2,2,1,1] generating graphics... => 150
[6,2,1,1,1,1] generating graphics... => 271
[6,1,1,1,1,1,1] generating graphics... => 499
[5,5,2] generating graphics... => 29
[5,5,1,1] generating graphics... => 50
[5,4,3] generating graphics... => 37
[5,4,2,1] generating graphics... => 82
[5,4,1,1,1] generating graphics... => 145
[5,3,3,1] generating graphics... => 96
[5,3,2,2] generating graphics... => 126
[5,3,2,1,1] generating graphics... => 223
[5,3,1,1,1,1] generating graphics... => 402
[5,2,2,2,1] generating graphics... => 297
[5,2,2,1,1,1] generating graphics... => 538
[5,2,1,1,1,1,1] generating graphics... => 989
[5,1,1,1,1,1,1,1] generating graphics... => 1842
[4,4,4] generating graphics... => 42
[4,4,3,1] generating graphics... => 110
[4,4,2,2] generating graphics... => 146
[4,4,2,1,1] generating graphics... => 259
[4,4,1,1,1,1] generating graphics... => 470
[4,3,3,2] generating graphics... => 175
[4,3,3,1,1] generating graphics... => 311
[4,3,2,2,1] generating graphics... => 420
[4,3,2,1,1,1] generating graphics... => 765
[4,3,1,1,1,1,1] generating graphics... => 1414
[4,2,2,2,2] generating graphics... => 572
[4,2,2,2,1,1] generating graphics... => 1046
[4,2,2,1,1,1,1] generating graphics... => 1941
[4,2,1,1,1,1,1,1] generating graphics... => 3643
[4,1,1,1,1,1,1,1,1] generating graphics... => 6904
[3,3,3,3] generating graphics... => 214
[3,3,3,2,1] generating graphics... => 517
[3,3,3,1,1,1] generating graphics... => 944
[3,3,2,2,2] generating graphics... => 710
[3,3,2,2,1,1] generating graphics... => 1306
[3,3,2,1,1,1,1] generating graphics... => 2436
[3,3,1,1,1,1,1,1] generating graphics... => 4600
[3,2,2,2,2,1] generating graphics... => 1824
[3,2,2,2,1,1,1] generating graphics... => 3425
[3,2,2,1,1,1,1,1] generating graphics... => 6508
[3,2,1,1,1,1,1,1,1] generating graphics... => 12498
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 24232
[2,2,2,2,2,2] generating graphics... => 2578
[2,2,2,2,2,1,1] generating graphics... => 4876
[2,2,2,2,1,1,1,1] generating graphics... => 9340
[2,2,2,1,1,1,1,1,1] generating graphics... => 18092
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 35420
[2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 70076
[1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 140152
click to show generating function       
Description
The sum of the entries in the column specified by the partition of the change of basis matrix from elementary symmetric functions to Schur symmetric functions.
For example, $e_{22} = s_{1111} + s_{211} + s_{22}$, so the statistic on the partition $22$ is $3$.
References
[1] a(n)= sum of entries of n-th Kostka matrix for the partitions of n. OEIS:A178718
Code
def statistic(mu):
    s = SymmetricFunctions(ZZ).s()
    e = SymmetricFunctions(ZZ).e()
    return sum(coeff for _, coeff in s(e(mu)))
Created
May 20, 2017 at 17:44 by Martin Rubey
Updated
Oct 31, 2017 at 08:10 by Martin Rubey