Identifier
Identifier
Values
[2] generating graphics... => 0
[1,1] generating graphics... => 1
[3] generating graphics... => 1
[2,1] generating graphics... => 1
[1,1,1] generating graphics... => 1
[4] generating graphics... => 0
[3,1] generating graphics... => 2
[2,2] generating graphics... => 1
[2,1,1] generating graphics... => 2
[1,1,1,1] generating graphics... => 1
[5] generating graphics... => 1
[4,1] generating graphics... => 2
[3,2] generating graphics... => 3
[3,1,1] generating graphics... => 4
[2,2,1] generating graphics... => 3
[2,1,1,1] generating graphics... => 3
[1,1,1,1,1] generating graphics... => 1
[6] generating graphics... => 0
[5,1] generating graphics... => 3
[4,2] generating graphics... => 5
[4,1,1] generating graphics... => 6
[3,3] generating graphics... => 3
[3,2,1] generating graphics... => 10
[3,1,1,1] generating graphics... => 7
[2,2,2] generating graphics... => 3
[2,2,1,1] generating graphics... => 6
[2,1,1,1,1] generating graphics... => 4
[1,1,1,1,1,1] generating graphics... => 1
[7] generating graphics... => 1
[6,1] generating graphics... => 3
[5,2] generating graphics... => 8
[5,1,1] generating graphics... => 9
[4,3] generating graphics... => 8
[4,2,1] generating graphics... => 21
[4,1,1,1] generating graphics... => 13
[3,3,1] generating graphics... => 13
[3,2,2] generating graphics... => 13
[3,2,1,1] generating graphics... => 23
[3,1,1,1,1] generating graphics... => 11
[2,2,2,1] generating graphics... => 9
[2,2,1,1,1] generating graphics... => 10
[2,1,1,1,1,1] generating graphics... => 5
[1,1,1,1,1,1,1] generating graphics... => 1
[8] generating graphics... => 0
[7,1] generating graphics... => 4
[6,2] generating graphics... => 11
[6,1,1] generating graphics... => 12
[5,3] generating graphics... => 16
[5,2,1] generating graphics... => 38
[5,1,1,1] generating graphics... => 22
[4,4] generating graphics... => 8
[4,3,1] generating graphics... => 42
[4,2,2] generating graphics... => 34
[4,2,1,1] generating graphics... => 57
[4,1,1,1,1] generating graphics... => 24
[3,3,2] generating graphics... => 26
[3,3,1,1] generating graphics... => 36
[3,2,2,1] generating graphics... => 45
[3,2,1,1,1] generating graphics... => 44
[3,1,1,1,1,1] generating graphics... => 16
[2,2,2,2] generating graphics... => 9
[2,2,2,1,1] generating graphics... => 19
[2,2,1,1,1,1] generating graphics... => 15
[2,1,1,1,1,1,1] generating graphics... => 6
[1,1,1,1,1,1,1,1] generating graphics... => 1
[9] generating graphics... => 1
[8,1] generating graphics... => 4
[7,2] generating graphics... => 15
[7,1,1] generating graphics... => 16
[6,3] generating graphics... => 27
[6,2,1] generating graphics... => 61
[6,1,1,1] generating graphics... => 34
[5,4] generating graphics... => 24
[5,3,1] generating graphics... => 96
[5,2,2] generating graphics... => 72
[5,2,1,1] generating graphics... => 117
[5,1,1,1,1] generating graphics... => 46
[4,4,1] generating graphics... => 50
[4,3,2] generating graphics... => 102
[4,3,1,1] generating graphics... => 135
[4,2,2,1] generating graphics... => 136
[4,2,1,1,1] generating graphics... => 125
[4,1,1,1,1,1] generating graphics... => 40
[3,3,3] generating graphics... => 26
[3,3,2,1] generating graphics... => 107
[3,3,1,1,1] generating graphics... => 80
[3,2,2,2] generating graphics... => 54
[3,2,2,1,1] generating graphics... => 108
[3,2,1,1,1,1] generating graphics... => 75
[3,1,1,1,1,1,1] generating graphics... => 22
[2,2,2,2,1] generating graphics... => 28
[2,2,2,1,1,1] generating graphics... => 34
[2,2,1,1,1,1,1] generating graphics... => 21
[2,1,1,1,1,1,1,1] generating graphics... => 7
[1,1,1,1,1,1,1,1,1] generating graphics... => 1
[10] generating graphics... => 0
[9,1] generating graphics... => 5
[8,2] generating graphics... => 19
[8,1,1] generating graphics... => 20
[7,3] generating graphics... => 42
[7,2,1] generating graphics... => 92
[7,1,1,1] generating graphics... => 50
[6,4] generating graphics... => 51
[6,3,1] generating graphics... => 184
[6,2,2] generating graphics... => 133
[6,2,1,1] generating graphics... => 212
[6,1,1,1,1] generating graphics... => 80
[5,5] generating graphics... => 24
[5,4,1] generating graphics... => 170
[5,3,2] generating graphics... => 270
[5,3,1,1] generating graphics... => 348
[5,2,2,1] generating graphics... => 325
[5,2,1,1,1] generating graphics... => 288
[5,1,1,1,1,1] generating graphics... => 86
[4,4,2] generating graphics... => 152
[4,4,1,1] generating graphics... => 185
[4,3,3] generating graphics... => 128
[4,3,2,1] generating graphics... => 480
[4,3,1,1,1] generating graphics... => 340
[4,2,2,2] generating graphics... => 190
[4,2,2,1,1] generating graphics... => 369
[4,2,1,1,1,1] generating graphics... => 240
[4,1,1,1,1,1,1] generating graphics... => 62
[3,3,3,1] generating graphics... => 133
[3,3,2,2] generating graphics... => 161
[3,3,2,1,1] generating graphics... => 295
[3,3,1,1,1,1] generating graphics... => 155
[3,2,2,2,1] generating graphics... => 190
[3,2,2,1,1,1] generating graphics... => 217
[3,2,1,1,1,1,1] generating graphics... => 118
[3,1,1,1,1,1,1,1] generating graphics... => 29
[2,2,2,2,2] generating graphics... => 28
[2,2,2,2,1,1] generating graphics... => 62
[2,2,2,1,1,1,1] generating graphics... => 55
[2,2,1,1,1,1,1,1] generating graphics... => 28
[2,1,1,1,1,1,1,1,1] generating graphics... => 8
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[11] generating graphics... => 1
[10,1] generating graphics... => 5
[9,2] generating graphics... => 24
[9,1,1] generating graphics... => 25
[8,3] generating graphics... => 61
[8,2,1] generating graphics... => 131
[8,1,1,1] generating graphics... => 70
[7,4] generating graphics... => 93
[7,3,1] generating graphics... => 318
[7,2,2] generating graphics... => 225
[7,2,1,1] generating graphics... => 354
[7,1,1,1,1] generating graphics... => 130
[6,5] generating graphics... => 75
[6,4,1] generating graphics... => 405
[6,3,2] generating graphics... => 587
[6,3,1,1] generating graphics... => 744
[6,2,2,1] generating graphics... => 670
[6,2,1,1,1] generating graphics... => 580
[6,1,1,1,1,1] generating graphics... => 166
[5,5,1] generating graphics... => 194
[5,4,2] generating graphics... => 592
[5,4,1,1] generating graphics... => 703
[5,3,3] generating graphics... => 398
[5,3,2,1] generating graphics... => 1423
[5,3,1,1,1] generating graphics... => 976
[5,2,2,2] generating graphics... => 515
[5,2,2,1,1] generating graphics... => 982
[5,2,1,1,1,1] generating graphics... => 614
[5,1,1,1,1,1,1] generating graphics... => 148
[4,4,3] generating graphics... => 280
[4,4,2,1] generating graphics... => 817
[4,4,1,1,1] generating graphics... => 525
[4,3,3,1] generating graphics... => 741
[4,3,2,2] generating graphics... => 831
[4,3,2,1,1] generating graphics... => 1484
[4,3,1,1,1,1] generating graphics... => 735
[4,2,2,2,1] generating graphics... => 749
[4,2,2,1,1,1] generating graphics... => 826
[4,2,1,1,1,1,1] generating graphics... => 420
[4,1,1,1,1,1,1,1] generating graphics... => 91
[3,3,3,2] generating graphics... => 294
[3,3,3,1,1] generating graphics... => 428
[3,3,2,2,1] generating graphics... => 646
[3,3,2,1,1,1] generating graphics... => 667
[3,3,1,1,1,1,1] generating graphics... => 273
[3,2,2,2,2] generating graphics... => 218
[3,2,2,2,1,1] generating graphics... => 469
[3,2,2,1,1,1,1] generating graphics... => 390
[3,2,1,1,1,1,1,1] generating graphics... => 175
[3,1,1,1,1,1,1,1,1] generating graphics... => 37
[2,2,2,2,2,1] generating graphics... => 90
[2,2,2,2,1,1,1] generating graphics... => 117
[2,2,2,1,1,1,1,1] generating graphics... => 83
[2,2,1,1,1,1,1,1,1] generating graphics... => 36
[2,1,1,1,1,1,1,1,1,1] generating graphics... => 9
[1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[12] generating graphics... => 0
[11,1] generating graphics... => 6
[10,2] generating graphics... => 29
[10,1,1] generating graphics... => 30
[9,3] generating graphics... => 85
[9,2,1] generating graphics... => 180
[9,1,1,1] generating graphics... => 95
[8,4] generating graphics... => 154
[8,3,1] generating graphics... => 510
[8,2,2] generating graphics... => 356
[8,2,1,1] generating graphics... => 555
[8,1,1,1,1] generating graphics... => 200
[7,5] generating graphics... => 168
[7,4,1] generating graphics... => 816
[7,3,2] generating graphics... => 1130
[7,3,1,1] generating graphics... => 1416
[7,2,2,1] generating graphics... => 1249
[7,2,1,1,1] generating graphics... => 1064
[7,1,1,1,1,1] generating graphics... => 296
[6,6] generating graphics... => 75
[6,5,1] generating graphics... => 674
[6,4,2] generating graphics... => 1584
[6,4,1,1] generating graphics... => 1852
[6,3,3] generating graphics... => 985
[6,3,2,1] generating graphics... => 3424
[6,3,1,1,1] generating graphics... => 2300
[6,2,2,2] generating graphics... => 1185
[6,2,2,1,1] generating graphics... => 2232
[6,2,1,1,1,1] generating graphics... => 1360
[6,1,1,1,1,1,1] generating graphics... => 314
[5,5,2] generating graphics... => 786
[5,5,1,1] generating graphics... => 897
[5,4,3] generating graphics... => 1270
[5,4,2,1] generating graphics... => 3535
[5,4,1,1,1] generating graphics... => 2204
[5,3,3,1] generating graphics... => 2562
[5,3,2,2] generating graphics... => 2769
[5,3,2,1,1] generating graphics... => 4865
[5,3,1,1,1,1] generating graphics... => 2325
[5,2,2,2,1] generating graphics... => 2246
[5,2,2,1,1,1] generating graphics... => 2422
[5,2,1,1,1,1,1] generating graphics... => 1182
[5,1,1,1,1,1,1,1] generating graphics... => 239
[4,4,4] generating graphics... => 280
[4,4,3,1] generating graphics... => 1838
[4,4,2,2] generating graphics... => 1648
[4,4,2,1,1] generating graphics... => 2826
[4,4,1,1,1,1] generating graphics... => 1260
[4,3,3,2] generating graphics... => 1866
[4,3,3,1,1] generating graphics... => 2653
[4,3,2,2,1] generating graphics... => 3710
[4,3,2,1,1,1] generating graphics... => 3712
[4,3,1,1,1,1,1] generating graphics... => 1428
[4,2,2,2,2] generating graphics... => 967
[4,2,2,2,1,1] generating graphics... => 2044
[4,2,2,1,1,1,1] generating graphics... => 1636
[4,2,1,1,1,1,1,1] generating graphics... => 686
[4,1,1,1,1,1,1,1,1] generating graphics... => 128
[3,3,3,3] generating graphics... => 294
[3,3,3,2,1] generating graphics... => 1368
[3,3,3,1,1,1] generating graphics... => 1095
[3,3,2,2,2] generating graphics... => 864
[3,3,2,2,1,1] generating graphics... => 1782
[3,3,2,1,1,1,1] generating graphics... => 1330
[3,3,1,1,1,1,1,1] generating graphics... => 448
[3,2,2,2,2,1] generating graphics... => 777
[3,2,2,2,1,1,1] generating graphics... => 976
[3,2,2,1,1,1,1,1] generating graphics... => 648
[3,2,1,1,1,1,1,1,1] generating graphics... => 248
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 46
[2,2,2,2,2,2] generating graphics... => 90
[2,2,2,2,2,1,1] generating graphics... => 207
[2,2,2,2,1,1,1,1] generating graphics... => 200
[2,2,2,1,1,1,1,1,1] generating graphics... => 119
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 45
[2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 10
[1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
click to show generating function       
Description
The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd.
To be precise, this is given for a partition $\lambda \vdash n$ by the number of standard tableaux $T$ of shape $\lambda$ such that $\min\big( \operatorname{Des}(T) \cup \{n\} \big)$ is odd.
The case of an even minimum is St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even..
Code
def statistic(L):
    n = sum(L)
    return sum( 1 for SYT in StandardTableaux(L) if is_odd(min( SYT.standard_descents() + [n] )) )

Created
Oct 12, 2016 at 15:26 by Christian Stump
Updated
Oct 12, 2016 at 15:34 by Christian Stump