Identifier
Identifier
Values
[] generating graphics... => 1
[1] generating graphics... => 1
[2] generating graphics... => 0
[1,1] generating graphics... => 1
[3] generating graphics... => 0
[2,1] generating graphics... => 1
[1,1,1] generating graphics... => 1
[4] generating graphics... => 0
[3,1] generating graphics... => 0
[2,2] generating graphics... => 1
[2,1,1] generating graphics... => 2
[1,1,1,1] generating graphics... => 1
[5] generating graphics... => 0
[4,1] generating graphics... => 0
[3,2] generating graphics... => 1
[3,1,1] generating graphics... => 1
[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... => 0
[4,2] generating graphics... => 0
[4,1,1] generating graphics... => 0
[3,3] generating graphics... => 1
[3,2,1] generating graphics... => 5
[3,1,1,1] generating graphics... => 3
[2,2,2] generating graphics... => 2
[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... => 0
[6,1] generating graphics... => 0
[5,2] generating graphics... => 0
[5,1,1] generating graphics... => 0
[4,3] generating graphics... => 1
[4,2,1] generating graphics... => 2
[4,1,1,1] generating graphics... => 1
[3,3,1] generating graphics... => 5
[3,2,2] generating graphics... => 6
[3,2,1,1] generating graphics... => 14
[3,1,1,1,1] generating graphics... => 6
[2,2,2,1] generating graphics... => 8
[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... => 0
[6,2] generating graphics... => 0
[6,1,1] generating graphics... => 0
[5,3] generating graphics... => 0
[5,2,1] generating graphics... => 0
[5,1,1,1] generating graphics... => 0
[4,4] generating graphics... => 1
[4,3,1] generating graphics... => 8
[4,2,2] generating graphics... => 6
[4,2,1,1] generating graphics... => 11
[4,1,1,1,1] generating graphics... => 4
[3,3,2] generating graphics... => 10
[3,3,1,1] generating graphics... => 16
[3,2,2,1] generating graphics... => 28
[3,2,1,1,1] generating graphics... => 30
[3,1,1,1,1,1] generating graphics... => 10
[2,2,2,2] generating graphics... => 6
[2,2,2,1,1] generating graphics... => 18
[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... => 0
[8,1] generating graphics... => 0
[7,2] generating graphics... => 0
[7,1,1] generating graphics... => 0
[6,3] generating graphics... => 0
[6,2,1] generating graphics... => 0
[6,1,1,1] generating graphics... => 0
[5,4] generating graphics... => 1
[5,3,1] generating graphics... => 3
[5,2,2] generating graphics... => 2
[5,2,1,1] generating graphics... => 3
[5,1,1,1,1] generating graphics... => 1
[4,4,1] generating graphics... => 7
[4,3,2] generating graphics... => 23
[4,3,1,1] generating graphics... => 34
[4,2,2,1] generating graphics... => 37
[4,2,1,1,1] generating graphics... => 35
[4,1,1,1,1,1] generating graphics... => 10
[3,3,3] generating graphics... => 6
[3,3,2,1] generating graphics... => 54
[3,3,1,1,1] generating graphics... => 40
[3,2,2,2] generating graphics... => 28
[3,2,2,1,1] generating graphics... => 76
[3,2,1,1,1,1] generating graphics... => 55
[3,1,1,1,1,1,1] generating graphics... => 15
[2,2,2,2,1] generating graphics... => 24
[2,2,2,1,1,1] generating graphics... => 33
[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... => 0
[8,2] generating graphics... => 0
[8,1,1] generating graphics... => 0
[7,3] generating graphics... => 0
[7,2,1] generating graphics... => 0
[7,1,1,1] generating graphics... => 0
[6,4] generating graphics... => 0
[6,3,1] generating graphics... => 0
[6,2,2] generating graphics... => 0
[6,2,1,1] generating graphics... => 0
[6,1,1,1,1] generating graphics... => 0
[5,5] generating graphics... => 1
[5,4,1] generating graphics... => 11
[5,3,2] generating graphics... => 18
[5,3,1,1] generating graphics... => 24
[5,2,2,1] generating graphics... => 22
[5,2,1,1,1] generating graphics... => 19
[5,1,1,1,1,1] generating graphics... => 5
[4,4,2] generating graphics... => 23
[4,4,1,1] generating graphics... => 31
[4,3,3] generating graphics... => 22
[4,3,2,1] generating graphics... => 148
[4,3,1,1,1] generating graphics... => 105
[4,2,2,2] generating graphics... => 53
[4,2,2,1,1] generating graphics... => 130
[4,2,1,1,1,1] generating graphics... => 85
[4,1,1,1,1,1,1] generating graphics... => 20
[3,3,3,1] generating graphics... => 44
[3,3,2,2] generating graphics... => 72
[3,3,2,1,1] generating graphics... => 170
[3,3,1,1,1,1] generating graphics... => 85
[3,2,2,2,1] generating graphics... => 128
[3,2,2,1,1,1] generating graphics... => 164
[3,2,1,1,1,1,1] generating graphics... => 91
[3,1,1,1,1,1,1,1] generating graphics... => 21
[2,2,2,2,2] generating graphics... => 18
[2,2,2,2,1,1] generating graphics... => 57
[2,2,2,1,1,1,1] generating graphics... => 54
[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... => 0
[10,1] generating graphics... => 0
[9,2] generating graphics... => 0
[9,1,1] generating graphics... => 0
[8,3] generating graphics... => 0
[8,2,1] generating graphics... => 0
[8,1,1,1] generating graphics... => 0
[7,4] generating graphics... => 0
[7,3,1] generating graphics... => 0
[7,2,2] generating graphics... => 0
[7,2,1,1] generating graphics... => 0
[7,1,1,1,1] generating graphics... => 0
[6,5] generating graphics... => 1
[6,4,1] generating graphics... => 4
[6,3,2] generating graphics... => 5
[6,3,1,1] generating graphics... => 6
[6,2,2,1] generating graphics... => 5
[6,2,1,1,1] generating graphics... => 4
[6,1,1,1,1,1] generating graphics... => 1
[5,5,1] generating graphics... => 9
[5,4,2] generating graphics... => 49
[5,4,1,1] generating graphics... => 63
[5,3,3] generating graphics... => 31
[5,3,2,1] generating graphics... => 158
[5,3,1,1,1] generating graphics... => 107
[5,2,2,2] generating graphics... => 51
[5,2,2,1,1] generating graphics... => 113
[5,2,1,1,1,1] generating graphics... => 69
[5,1,1,1,1,1,1] generating graphics... => 15
[4,4,3] generating graphics... => 39
[4,4,2,1] generating graphics... => 165
[4,4,1,1,1] generating graphics... => 105
[4,3,3,1] generating graphics... => 180
[4,3,2,2] generating graphics... => 250
[4,3,2,1,1] generating graphics... => 553
[4,3,1,1,1,1] generating graphics... => 265
[4,2,2,2,1] generating graphics... => 287
[4,2,2,1,1,1] generating graphics... => 346
[4,2,1,1,1,1,1] generating graphics... => 175
[4,1,1,1,1,1,1,1] generating graphics... => 35
[3,3,3,2] generating graphics... => 110
[3,3,3,1,1] generating graphics... => 174
[3,3,2,2,1] generating graphics... => 370
[3,3,2,1,1,1] generating graphics... => 419
[3,3,1,1,1,1,1] generating graphics... => 161
[3,2,2,2,2] generating graphics... => 118
[3,2,2,2,1,1] generating graphics... => 349
[3,2,2,1,1,1,1] generating graphics... => 309
[3,2,1,1,1,1,1,1] generating graphics... => 140
[3,1,1,1,1,1,1,1,1] generating graphics... => 28
[2,2,2,2,2,1] generating graphics... => 75
[2,2,2,2,1,1,1] generating graphics... => 111
[2,2,2,1,1,1,1,1] generating graphics... => 82
[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... => 0
[10,2] generating graphics... => 0
[10,1,1] generating graphics... => 0
[9,3] generating graphics... => 0
[9,2,1] generating graphics... => 0
[9,1,1,1] generating graphics... => 0
[8,4] generating graphics... => 0
[8,3,1] generating graphics... => 0
[8,2,2] generating graphics... => 0
[8,2,1,1] generating graphics... => 0
[8,1,1,1,1] generating graphics... => 0
[7,5] generating graphics... => 0
[7,4,1] generating graphics... => 0
[7,3,2] generating graphics... => 0
[7,3,1,1] generating graphics... => 0
[7,2,2,1] generating graphics... => 0
[7,2,1,1,1] generating graphics... => 0
[7,1,1,1,1,1] generating graphics... => 0
[6,6] generating graphics... => 1
[6,5,1] generating graphics... => 14
[6,4,2] generating graphics... => 35
[6,4,1,1] generating graphics... => 42
[6,3,3] generating graphics... => 20
[6,3,2,1] generating graphics... => 80
[6,3,1,1,1] generating graphics... => 52
[6,2,2,2] generating graphics... => 25
[6,2,2,1,1] generating graphics... => 50
[6,2,1,1,1,1] generating graphics... => 29
[6,1,1,1,1,1,1] generating graphics... => 6
[5,5,2] generating graphics... => 41
[5,5,1,1] generating graphics... => 51
[5,4,3] generating graphics... => 109
[5,4,2,1] generating graphics... => 413
[5,4,1,1,1] generating graphics... => 257
[5,3,3,1] generating graphics... => 301
[5,3,2,2] generating graphics... => 369
[5,3,2,1,1] generating graphics... => 761
[5,3,1,1,1,1] generating graphics... => 351
[5,2,2,2,1] generating graphics... => 347
[5,2,2,1,1,1] generating graphics... => 397
[5,2,1,1,1,1,1] generating graphics... => 189
[5,1,1,1,1,1,1,1] generating graphics... => 35
[4,4,4] generating graphics... => 22
[4,4,3,1] generating graphics... => 353
[4,4,2,2] generating graphics... => 339
[4,4,2,1,1] generating graphics... => 693
[4,4,1,1,1,1] generating graphics... => 295
[4,3,3,2] generating graphics... => 518
[4,3,3,1,1] generating graphics... => 802
[4,3,2,2,1] generating graphics... => 1460
[4,3,2,1,1,1] generating graphics... => 1583
[4,3,1,1,1,1,1] generating graphics... => 581
[4,2,2,2,2] generating graphics... => 334
[4,2,2,2,1,1] generating graphics... => 925
[4,2,2,1,1,1,1] generating graphics... => 776
[4,2,1,1,1,1,1,1] generating graphics... => 322
[4,1,1,1,1,1,1,1,1] generating graphics... => 56
[3,3,3,3] generating graphics... => 72
[3,3,3,2,1] generating graphics... => 654
[3,3,3,1,1,1] generating graphics... => 508
[3,3,2,2,2] generating graphics... => 416
[3,3,2,2,1,1] generating graphics... => 1138
[3,3,2,1,1,1,1] generating graphics... => 889
[3,3,1,1,1,1,1,1] generating graphics... => 280
[3,2,2,2,2,1] generating graphics... => 542
[3,2,2,2,1,1,1] generating graphics... => 769
[3,2,2,1,1,1,1,1] generating graphics... => 531
[3,2,1,1,1,1,1,1,1] generating graphics... => 204
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 36
[2,2,2,2,2,2] generating graphics... => 57
[2,2,2,2,2,1,1] generating graphics... => 186
[2,2,2,2,1,1,1,1] generating graphics... => 193
[2,2,2,1,1,1,1,1,1] generating graphics... => 118
[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 Young tableaux for an integer partition such that no two consecutive entries appear in the same row.
Summing over all partitions of $n$ yields the sequence
$$1, 1, 1, 2, 4, 9, 22, 59, 170, 516, 1658, \dots$$
which is oeis:A237770.
The references in this sequence of the OEIS indicate a connection with Baxter permutations.
References
[1] Dulucq, S., Guibert, O. Stack words, standard tableaux and Baxter permutations MathSciNet:1417289 DOI:10.1016/s0012-365x(96)83009-3
Code
def statistic(x):
    l = [any(any(f == e+1 for (e,f) in zip(row, row[1:])) 
             for row in T) 
         for T in StandardTableaux(x)]
    return l.count(False)
Created
Aug 21, 2014 at 14:22 by Per Alexandersson
Updated
Oct 29, 2017 at 16:35 by Martin Rubey