Identifier
Identifier
Values
[2] generating graphics... => 1
[1,1] generating graphics... => 3
[3] generating graphics... => 1
[2,1] generating graphics... => 4
[1,1,1] generating graphics... => 10
[4] generating graphics... => 1
[3,1] generating graphics... => 5
[2,2] generating graphics... => 9
[2,1,1] generating graphics... => 20
[1,1,1,1] generating graphics... => 47
[5] generating graphics... => 1
[4,1] generating graphics... => 6
[3,2] generating graphics... => 14
[3,1,1] generating graphics... => 30
[2,2,1] generating graphics... => 50
[2,1,1,1] generating graphics... => 110
[1,1,1,1,1] generating graphics... => 246
[6] generating graphics... => 1
[5,1] generating graphics... => 7
[4,2] generating graphics... => 20
[4,1,1] generating graphics... => 42
[3,3] generating graphics... => 29
[3,2,1] generating graphics... => 97
[3,1,1,1] generating graphics... => 206
[2,2,2] generating graphics... => 157
[2,2,1,1] generating graphics... => 338
[2,1,1,1,1] generating graphics... => 732
[1,1,1,1,1,1] generating graphics... => 1602
[7] generating graphics... => 1
[6,1] generating graphics... => 8
[5,2] generating graphics... => 27
[5,1,1] generating graphics... => 56
[4,3] generating graphics... => 49
[4,2,1] generating graphics... => 159
[4,1,1,1] generating graphics... => 332
[3,3,1] generating graphics... => 224
[3,2,2] generating graphics... => 353
[3,2,1,1] generating graphics... => 743
[3,1,1,1,1] generating graphics... => 1568
[2,2,2,1] generating graphics... => 1184
[2,2,1,1,1] generating graphics... => 2513
[2,1,1,1,1,1] generating graphics... => 5357
[1,1,1,1,1,1,1] generating graphics... => 11481
[8] generating graphics... => 1
[7,1] generating graphics... => 9
[6,2] generating graphics... => 35
[6,1,1] generating graphics... => 72
[5,3] generating graphics... => 76
[5,2,1] generating graphics... => 242
[5,1,1,1] generating graphics... => 500
[4,4] generating graphics... => 99
[4,3,1] generating graphics... => 436
[4,2,2] generating graphics... => 677
[4,2,1,1] generating graphics... => 1405
[4,1,1,1,1] generating graphics... => 2920
[3,3,2] generating graphics... => 943
[3,3,1,1] generating graphics... => 1965
[3,2,2,1] generating graphics... => 3078
[3,2,1,1,1] generating graphics... => 6437
[3,1,1,1,1,1] generating graphics... => 13487
[2,2,2,2] generating graphics... => 4845
[2,2,2,1,1] generating graphics... => 10163
[2,2,1,1,1,1] generating graphics... => 21378
[2,1,1,1,1,1,1] generating graphics... => 45104
[1,1,1,1,1,1,1,1] generating graphics... => 95503
[9] generating graphics... => 1
[8,1] generating graphics... => 10
[7,2] generating graphics... => 44
[7,1,1] generating graphics... => 90
[6,3] generating graphics... => 111
[6,2,1] generating graphics... => 349
[6,1,1,1] generating graphics... => 716
[5,4] generating graphics... => 175
[5,3,1] generating graphics... => 754
[5,2,2] generating graphics... => 1161
[5,2,1,1] generating graphics... => 2389
[5,1,1,1,1] generating graphics... => 4920
[4,4,1] generating graphics... => 972
[4,3,2] generating graphics... => 2059
[4,3,1,1] generating graphics... => 4249
[4,2,2,1] generating graphics... => 6577
[4,2,1,1,1] generating graphics... => 13599
[4,1,1,1,1,1] generating graphics... => 28147
[3,3,3] generating graphics... => 2836
[3,3,2,1] generating graphics... => 9095
[3,3,1,1,1] generating graphics... => 18843
[3,2,2,2] generating graphics... => 14139
[3,2,2,1,1] generating graphics... => 29338
[3,2,1,1,1,1] generating graphics... => 60962
[3,1,1,1,1,1,1] generating graphics... => 126866
[2,2,2,2,1] generating graphics... => 45796
[2,2,2,1,1,1] generating graphics... => 95359
[2,2,1,1,1,1,1] generating graphics... => 198920
[2,1,1,1,1,1,1,1] generating graphics... => 415781
[1,1,1,1,1,1,1,1,1] generating graphics... => 871030
[10] generating graphics... => 1
[9,1] generating graphics... => 11
[8,2] generating graphics... => 54
[8,1,1] generating graphics... => 110
[7,3] generating graphics... => 155
[7,2,1] generating graphics... => 483
[7,1,1,1] generating graphics... => 986
[6,4] generating graphics... => 286
[6,3,1] generating graphics... => 1214
[6,2,2] generating graphics... => 1859
[6,2,1,1] generating graphics... => 3803
[6,1,1,1,1] generating graphics... => 7784
[5,5] generating graphics... => 351
[5,4,1] generating graphics... => 1906
[5,3,2] generating graphics... => 3984
[5,3,1,1] generating graphics... => 8166
[5,2,2,1] generating graphics... => 12546
[5,2,1,1,1] generating graphics... => 25746
[5,1,1,1,1,1] generating graphics... => 52867
[4,4,2] generating graphics... => 5111
[4,4,1,1] generating graphics... => 10490
[4,3,3] generating graphics... => 6986
[4,3,2,1] generating graphics... => 22101
[4,3,1,1,1] generating graphics... => 45457
[4,2,2,2] generating graphics... => 34071
[4,2,2,1,1] generating graphics... => 70132
[4,2,1,1,1,1] generating graphics... => 144471
[4,1,1,1,1,1,1] generating graphics... => 297848
[3,3,3,1] generating graphics... => 30326
[3,3,2,2] generating graphics... => 46830
[3,3,2,1,1] generating graphics... => 96519
[3,3,1,1,1,1] generating graphics... => 199122
[3,2,2,2,1] generating graphics... => 149384
[3,2,2,1,1,1] generating graphics... => 308537
[3,2,1,1,1,1,1] generating graphics... => 637937
[3,1,1,1,1,1,1,1] generating graphics... => 1320510
[2,2,2,2,2] generating graphics... => 231571
[2,2,2,2,1,1] generating graphics... => 478940
[2,2,2,1,1,1,1] generating graphics... => 991743
[2,2,1,1,1,1,1,1] generating graphics... => 2056300
[2,1,1,1,1,1,1,1,1] generating graphics... => 4269680
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 8879558
[11] generating graphics... => 1
[10,1] generating graphics... => 12
[9,2] generating graphics... => 65
[9,1,1] generating graphics... => 132
[8,3] generating graphics... => 209
[8,2,1] generating graphics... => 647
[8,1,1,1] generating graphics... => 1316
[7,4] generating graphics... => 441
[7,3,1] generating graphics... => 1852
[7,2,2] generating graphics... => 2825
[7,2,1,1] generating graphics... => 5755
[7,1,1,1,1] generating graphics... => 11728
[6,5] generating graphics... => 637
[6,4,1] generating graphics... => 3406
[6,3,2] generating graphics... => 7057
[6,3,1,1] generating graphics... => 14397
[6,2,2,1] generating graphics... => 22011
[6,2,1,1,1] generating graphics... => 44939
[6,1,1,1,1,1] generating graphics... => 91787
[5,5,1] generating graphics... => 4164
[5,4,2] generating graphics... => 11005
[5,4,1,1] generating graphics... => 22477
[5,3,3] generating graphics... => 14960
[5,3,2,1] generating graphics... => 46819
[5,3,1,1,1] generating graphics... => 95749
[5,2,2,2] generating graphics... => 71745
[5,2,2,1,1] generating graphics... => 146794
[5,2,1,1,1,1] generating graphics... => 300490
[5,1,1,1,1,1,1] generating graphics... => 615410
[4,4,3] generating graphics... => 19096
[4,4,2,1] generating graphics... => 59855
[4,4,1,1,1] generating graphics... => 122503
[4,3,3,1] generating graphics... => 81601
[4,3,2,2] generating graphics... => 125256
[4,3,2,1,1] generating graphics... => 256659
[4,3,1,1,1,1] generating graphics... => 526216
[4,2,2,2,1] generating graphics... => 394463
[4,2,2,1,1,1] generating graphics... => 809266
[4,2,1,1,1,1,1] generating graphics... => 1661295
[4,1,1,1,1,1,1,1] generating graphics... => 3412586
[3,3,3,2] generating graphics... => 171090
[3,3,3,1,1] generating graphics... => 350840
[3,3,2,2,1] generating graphics... => 539778
[3,3,2,1,1,1] generating graphics... => 1108391
[3,3,1,1,1,1,1] generating graphics... => 2277586
[3,2,2,2,2] generating graphics... => 831191
[3,2,2,2,1,1] generating graphics... => 1708151
[3,2,2,1,1,1,1] generating graphics... => 3512988
[3,2,1,1,1,1,1,1] generating graphics... => 7230549
[3,1,1,1,1,1,1,1,1] generating graphics... => 14894660
[2,2,2,2,2,1] generating graphics... => 2635257
[2,2,2,2,1,1,1] generating graphics... => 5424814
[2,2,2,1,1,1,1,1] generating graphics... => 11176952
[2,2,1,1,1,1,1,1,1] generating graphics... => 23049690
[2,1,1,1,1,1,1,1,1,1] generating graphics... => 47581727
[1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 98329551
[12] generating graphics... => 1
[11,1] generating graphics... => 13
[10,2] generating graphics... => 77
[10,1,1] generating graphics... => 156
[9,3] generating graphics... => 274
[9,2,1] generating graphics... => 844
[9,1,1,1] generating graphics... => 1712
[8,4] generating graphics... => 650
[8,3,1] generating graphics... => 2708
[8,2,2] generating graphics... => 4119
[8,2,1,1] generating graphics... => 8365
[8,1,1,1,1] generating graphics... => 16992
[7,5] generating graphics... => 1078
[7,4,1] generating graphics... => 5699
[7,3,2] generating graphics... => 11734
[7,3,1,1] generating graphics... => 23856
[7,2,2,1] generating graphics... => 36346
[7,2,1,1,1] generating graphics... => 73932
[7,1,1,1,1,1] generating graphics... => 150427
[6,6] generating graphics... => 1275
[6,5,1] generating graphics... => 8213
[6,4,2] generating graphics... => 21483
[6,4,1,1] generating graphics... => 43716
[6,3,3] generating graphics... => 29094
[6,3,2,1] generating graphics... => 90344
[6,3,1,1,1] generating graphics... => 183999
[6,2,2,2] generating graphics... => 137868
[6,2,2,1,1] generating graphics... => 280874
[6,2,1,1,1,1] generating graphics... => 572393
[6,1,1,1,1,1,1] generating graphics... => 1166852
[5,5,2] generating graphics... => 26205
[5,5,1,1] generating graphics... => 53351
[5,4,3] generating graphics... => 45124
[5,4,2,1] generating graphics... => 140381
[5,4,1,1,1] generating graphics... => 286170
[5,3,3,1] generating graphics... => 190523
[5,3,2,2] generating graphics... => 291162
[5,3,2,1,1] generating graphics... => 593962
[5,3,1,1,1,1] generating graphics... => 1212100
[5,2,2,2,1] generating graphics... => 908387
[5,2,2,1,1,1] generating graphics... => 1854456
[5,2,1,1,1,1,1] generating graphics... => 3787285
[5,1,1,1,1,1,1,1] generating graphics... => 7737676
[4,4,4] generating graphics... => 57385
[4,4,3,1] generating graphics... => 242689
[4,4,2,2] generating graphics... => 371122
[4,4,2,1,1] generating graphics... => 757490
[4,4,1,1,1,1] generating graphics... => 1546726
[4,3,3,2] generating graphics... => 504587
[4,3,3,1,1] generating graphics... => 1030376
[4,3,2,2,1] generating graphics... => 1577875
[4,3,2,1,1,1] generating graphics... => 3224913
[4,3,1,1,1,1,1] generating graphics... => 6594182
[4,2,2,2,2] generating graphics... => 2417525
[4,2,2,2,1,1] generating graphics... => 4943420
[4,2,2,1,1,1,1] generating graphics... => 10113232
[4,2,1,1,1,1,1,1] generating graphics... => 20699788
[4,1,1,1,1,1,1,1,1] generating graphics... => 42390004
[3,3,3,3] generating graphics... => 686557
[3,3,3,2,1] generating graphics... => 2149402
[3,3,3,1,1,1] generating graphics... => 4395584
[3,3,2,2,2] generating graphics... => 3295560
[3,3,2,2,1,1] generating graphics... => 6743185
[3,3,2,1,1,1,1] generating graphics... => 13804634
[3,3,1,1,1,1,1,1] generating graphics... => 28276134
[3,2,2,2,2,1] generating graphics... => 10351471
[3,2,2,2,1,1,1] generating graphics... => 21204493
[3,2,2,1,1,1,1,1] generating graphics... => 43461404
[3,2,1,1,1,1,1,1,1] generating graphics... => 89133888
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 182919233
[2,2,2,2,2,2] generating graphics... => 15902253
[2,2,2,2,2,1,1] generating graphics... => 32596683
[2,2,2,2,1,1,1,1] generating graphics... => 66858586
[2,2,2,1,1,1,1,1,1] generating graphics... => 137222522
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 281835366
[2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 579278088
[1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1191578522
click to show generating function       
Description
The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition.
This is also the sum of the entries in the column specified by the partition of the change of basis matrix from elementary symmetric functions to monomial symmetric functions.
References
[1] Number of different 0-1 matrices in which the number of 1's is n, with at least one 1 in each row and column. OEIS:A068313
Code
def statistic(mu):
    m = SymmetricFunctions(ZZ).m()
    e = SymmetricFunctions(ZZ).e()
    return sum(coeff for _, coeff in m(e(mu)))
Created
May 20, 2017 at 17:37 by Martin Rubey
Updated
May 20, 2017 at 22:45 by Martin Rubey