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... => 3
[1,1,1] generating graphics... => 6
[4] generating graphics... => 1
[3,1] generating graphics... => 4
[2,2] generating graphics... => 6
[2,1,1] generating graphics... => 12
[1,1,1,1] generating graphics... => 24
[5] generating graphics... => 1
[4,1] generating graphics... => 5
[3,2] generating graphics... => 10
[3,1,1] generating graphics... => 20
[2,2,1] generating graphics... => 30
[2,1,1,1] generating graphics... => 60
[1,1,1,1,1] generating graphics... => 120
[6] generating graphics... => 1
[5,1] generating graphics... => 6
[4,2] generating graphics... => 15
[4,1,1] generating graphics... => 30
[3,3] generating graphics... => 20
[3,2,1] generating graphics... => 60
[3,1,1,1] generating graphics... => 120
[2,2,2] generating graphics... => 90
[2,2,1,1] generating graphics... => 180
[2,1,1,1,1] generating graphics... => 360
[1,1,1,1,1,1] generating graphics... => 720
[7] generating graphics... => 1
[6,1] generating graphics... => 7
[5,2] generating graphics... => 21
[5,1,1] generating graphics... => 42
[4,3] generating graphics... => 35
[4,2,1] generating graphics... => 105
[4,1,1,1] generating graphics... => 210
[3,3,1] generating graphics... => 140
[3,2,2] generating graphics... => 210
[3,2,1,1] generating graphics... => 420
[3,1,1,1,1] generating graphics... => 840
[2,2,2,1] generating graphics... => 630
[2,2,1,1,1] generating graphics... => 1260
[2,1,1,1,1,1] generating graphics... => 2520
[1,1,1,1,1,1,1] generating graphics... => 5040
[8] generating graphics... => 1
[7,1] generating graphics... => 8
[6,2] generating graphics... => 28
[6,1,1] generating graphics... => 56
[5,3] generating graphics... => 56
[5,2,1] generating graphics... => 168
[5,1,1,1] generating graphics... => 336
[4,4] generating graphics... => 70
[4,3,1] generating graphics... => 280
[4,2,2] generating graphics... => 420
[4,2,1,1] generating graphics... => 840
[4,1,1,1,1] generating graphics... => 1680
[3,3,2] generating graphics... => 560
[3,3,1,1] generating graphics... => 1120
[3,2,2,1] generating graphics... => 1680
[3,2,1,1,1] generating graphics... => 3360
[3,1,1,1,1,1] generating graphics... => 6720
[2,2,2,2] generating graphics... => 2520
[2,2,2,1,1] generating graphics... => 5040
[2,2,1,1,1,1] generating graphics... => 10080
[2,1,1,1,1,1,1] generating graphics... => 20160
[1,1,1,1,1,1,1,1] generating graphics... => 40320
[9] generating graphics... => 1
[8,1] generating graphics... => 9
[7,2] generating graphics... => 36
[7,1,1] generating graphics... => 72
[6,3] generating graphics... => 84
[6,2,1] generating graphics... => 252
[6,1,1,1] generating graphics... => 504
[5,4] generating graphics... => 126
[5,3,1] generating graphics... => 504
[5,2,2] generating graphics... => 756
[5,2,1,1] generating graphics... => 1512
[5,1,1,1,1] generating graphics... => 3024
[4,4,1] generating graphics... => 630
[4,3,2] generating graphics... => 1260
[4,3,1,1] generating graphics... => 2520
[4,2,2,1] generating graphics... => 3780
[4,2,1,1,1] generating graphics... => 7560
[4,1,1,1,1,1] generating graphics... => 15120
[3,3,3] generating graphics... => 1680
[3,3,2,1] generating graphics... => 5040
[3,3,1,1,1] generating graphics... => 10080
[3,2,2,2] generating graphics... => 7560
[3,2,2,1,1] generating graphics... => 15120
[3,2,1,1,1,1] generating graphics... => 30240
[3,1,1,1,1,1,1] generating graphics... => 60480
[2,2,2,2,1] generating graphics... => 22680
[2,2,2,1,1,1] generating graphics... => 45360
[2,2,1,1,1,1,1] generating graphics... => 90720
[2,1,1,1,1,1,1,1] generating graphics... => 181440
[1,1,1,1,1,1,1,1,1] generating graphics... => 362880
[10] generating graphics... => 1
[9,1] generating graphics... => 10
[8,2] generating graphics... => 45
[8,1,1] generating graphics... => 90
[7,3] generating graphics... => 120
[7,2,1] generating graphics... => 360
[7,1,1,1] generating graphics... => 720
[6,4] generating graphics... => 210
[6,3,1] generating graphics... => 840
[6,2,2] generating graphics... => 1260
[6,2,1,1] generating graphics... => 2520
[6,1,1,1,1] generating graphics... => 5040
[5,5] generating graphics... => 252
[5,4,1] generating graphics... => 1260
[5,3,2] generating graphics... => 2520
[5,3,1,1] generating graphics... => 5040
[5,2,2,1] generating graphics... => 7560
[5,2,1,1,1] generating graphics... => 15120
[5,1,1,1,1,1] generating graphics... => 30240
[4,4,2] generating graphics... => 3150
[4,4,1,1] generating graphics... => 6300
[4,3,3] generating graphics... => 4200
[4,3,2,1] generating graphics... => 12600
[4,3,1,1,1] generating graphics... => 25200
[4,2,2,2] generating graphics... => 18900
[4,2,2,1,1] generating graphics... => 37800
[4,2,1,1,1,1] generating graphics... => 75600
[4,1,1,1,1,1,1] generating graphics... => 151200
[3,3,3,1] generating graphics... => 16800
[3,3,2,2] generating graphics... => 25200
[3,3,2,1,1] generating graphics... => 50400
[3,3,1,1,1,1] generating graphics... => 100800
[3,2,2,2,1] generating graphics... => 75600
[3,2,2,1,1,1] generating graphics... => 151200
[3,2,1,1,1,1,1] generating graphics... => 302400
[3,1,1,1,1,1,1,1] generating graphics... => 604800
[2,2,2,2,2] generating graphics... => 113400
[2,2,2,2,1,1] generating graphics... => 226800
[2,2,2,1,1,1,1] generating graphics... => 453600
[2,2,1,1,1,1,1,1] generating graphics... => 907200
[2,1,1,1,1,1,1,1,1] generating graphics... => 1814400
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 3628800
[11] generating graphics... => 1
[10,1] generating graphics... => 11
[9,2] generating graphics... => 55
[9,1,1] generating graphics... => 110
[8,3] generating graphics... => 165
[8,2,1] generating graphics... => 495
[8,1,1,1] generating graphics... => 990
[7,4] generating graphics... => 330
[7,3,1] generating graphics... => 1320
[7,2,2] generating graphics... => 1980
[7,2,1,1] generating graphics... => 3960
[7,1,1,1,1] generating graphics... => 7920
[6,5] generating graphics... => 462
[6,4,1] generating graphics... => 2310
[6,3,2] generating graphics... => 4620
[6,3,1,1] generating graphics... => 9240
[6,2,2,1] generating graphics... => 13860
[6,2,1,1,1] generating graphics... => 27720
[6,1,1,1,1,1] generating graphics... => 55440
[5,5,1] generating graphics... => 2772
[5,4,2] generating graphics... => 6930
[5,4,1,1] generating graphics... => 13860
[5,3,3] generating graphics... => 9240
[5,3,2,1] generating graphics... => 27720
[5,3,1,1,1] generating graphics... => 55440
[5,2,2,2] generating graphics... => 41580
[5,2,2,1,1] generating graphics... => 83160
[5,2,1,1,1,1] generating graphics... => 166320
[5,1,1,1,1,1,1] generating graphics... => 332640
[4,4,3] generating graphics... => 11550
[4,4,2,1] generating graphics... => 34650
[4,4,1,1,1] generating graphics... => 69300
[4,3,3,1] generating graphics... => 46200
[4,3,2,2] generating graphics... => 69300
[4,3,2,1,1] generating graphics... => 138600
[4,3,1,1,1,1] generating graphics... => 277200
[4,2,2,2,1] generating graphics... => 207900
[4,2,2,1,1,1] generating graphics... => 415800
[4,2,1,1,1,1,1] generating graphics... => 831600
[4,1,1,1,1,1,1,1] generating graphics... => 1663200
[3,3,3,2] generating graphics... => 92400
[3,3,3,1,1] generating graphics... => 184800
[3,3,2,2,1] generating graphics... => 277200
[3,3,2,1,1,1] generating graphics... => 554400
[3,3,1,1,1,1,1] generating graphics... => 1108800
[3,2,2,2,2] generating graphics... => 415800
[3,2,2,2,1,1] generating graphics... => 831600
[3,2,2,1,1,1,1] generating graphics... => 1663200
[3,2,1,1,1,1,1,1] generating graphics... => 3326400
[3,1,1,1,1,1,1,1,1] generating graphics... => 6652800
[2,2,2,2,2,1] generating graphics... => 1247400
[2,2,2,2,1,1,1] generating graphics... => 2494800
[2,2,2,1,1,1,1,1] generating graphics... => 4989600
[2,2,1,1,1,1,1,1,1] generating graphics... => 9979200
[12] generating graphics... => 1
[11,1] generating graphics... => 12
[10,2] generating graphics... => 66
[10,1,1] generating graphics... => 132
[9,3] generating graphics... => 220
[9,2,1] generating graphics... => 660
[9,1,1,1] generating graphics... => 1320
[8,4] generating graphics... => 495
[8,3,1] generating graphics... => 1980
[8,2,2] generating graphics... => 2970
[8,2,1,1] generating graphics... => 5940
[8,1,1,1,1] generating graphics... => 11880
[7,5] generating graphics... => 792
[7,4,1] generating graphics... => 3960
[7,3,2] generating graphics... => 7920
[7,3,1,1] generating graphics... => 15840
[7,2,2,1] generating graphics... => 23760
[7,2,1,1,1] generating graphics... => 47520
[7,1,1,1,1,1] generating graphics... => 95040
[6,6] generating graphics... => 924
[6,5,1] generating graphics... => 5544
[6,4,2] generating graphics... => 13860
[6,4,1,1] generating graphics... => 27720
[6,3,3] generating graphics... => 18480
[6,3,2,1] generating graphics... => 55440
[6,3,1,1,1] generating graphics... => 110880
[6,2,2,2] generating graphics... => 83160
[6,2,2,1,1] generating graphics... => 166320
[6,2,1,1,1,1] generating graphics... => 332640
[6,1,1,1,1,1,1] generating graphics... => 665280
[5,5,2] generating graphics... => 16632
[5,5,1,1] generating graphics... => 33264
[5,4,3] generating graphics... => 27720
[5,4,2,1] generating graphics... => 83160
[5,4,1,1,1] generating graphics... => 166320
[5,3,3,1] generating graphics... => 110880
[5,3,2,2] generating graphics... => 166320
[5,3,2,1,1] generating graphics... => 332640
[5,3,1,1,1,1] generating graphics... => 665280
[5,2,2,2,1] generating graphics... => 498960
[5,2,2,1,1,1] generating graphics... => 997920
[5,2,1,1,1,1,1] generating graphics... => 1995840
[5,1,1,1,1,1,1,1] generating graphics... => 3991680
[4,4,4] generating graphics... => 34650
[4,4,3,1] generating graphics... => 138600
[4,4,2,2] generating graphics... => 207900
[4,4,2,1,1] generating graphics... => 415800
[4,4,1,1,1,1] generating graphics... => 831600
[4,3,3,2] generating graphics... => 277200
[4,3,3,1,1] generating graphics... => 554400
[4,3,2,2,1] generating graphics... => 831600
[4,3,2,1,1,1] generating graphics... => 1663200
[4,3,1,1,1,1,1] generating graphics... => 3326400
[4,2,2,2,2] generating graphics... => 1247400
[4,2,2,2,1,1] generating graphics... => 2494800
[4,2,2,1,1,1,1] generating graphics... => 4989600
[4,2,1,1,1,1,1,1] generating graphics... => 9979200
[3,3,3,3] generating graphics... => 369600
[3,3,3,2,1] generating graphics... => 1108800
[3,3,3,1,1,1] generating graphics... => 2217600
[3,3,2,2,2] generating graphics... => 1663200
[3,3,2,2,1,1] generating graphics... => 3326400
[3,3,2,1,1,1,1] generating graphics... => 6652800
[3,2,2,2,2,1] generating graphics... => 4989600
[3,2,2,2,1,1,1] generating graphics... => 9979200
[2,2,2,2,2,2] generating graphics... => 7484400
[13] generating graphics... => 1
[12,1] generating graphics... => 13
[11,2] generating graphics... => 78
[11,1,1] generating graphics... => 156
[10,3] generating graphics... => 286
[10,2,1] generating graphics... => 858
[10,1,1,1] generating graphics... => 1716
[9,4] generating graphics... => 715
[9,3,1] generating graphics... => 2860
[9,2,2] generating graphics... => 4290
[9,2,1,1] generating graphics... => 8580
[9,1,1,1,1] generating graphics... => 17160
[8,5] generating graphics... => 1287
[8,4,1] generating graphics... => 6435
[8,3,2] generating graphics... => 12870
[8,3,1,1] generating graphics... => 25740
[8,2,2,1] generating graphics... => 38610
[8,2,1,1,1] generating graphics... => 77220
[8,1,1,1,1,1] generating graphics... => 154440
[7,6] generating graphics... => 1716
[7,5,1] generating graphics... => 10296
[7,4,2] generating graphics... => 25740
[7,4,1,1] generating graphics... => 51480
[7,3,3] generating graphics... => 34320
[7,3,2,1] generating graphics... => 102960
[7,3,1,1,1] generating graphics... => 205920
[7,2,2,2] generating graphics... => 154440
[7,2,2,1,1] generating graphics... => 308880
[7,2,1,1,1,1] generating graphics... => 617760
[7,1,1,1,1,1,1] generating graphics... => 1235520
[6,6,1] generating graphics... => 12012
[6,5,2] generating graphics... => 36036
[6,5,1,1] generating graphics... => 72072
[6,4,3] generating graphics... => 60060
[6,4,2,1] generating graphics... => 180180
[6,4,1,1,1] generating graphics... => 360360
[6,3,3,1] generating graphics... => 240240
[6,3,2,2] generating graphics... => 360360
[6,3,2,1,1] generating graphics... => 720720
[6,3,1,1,1,1] generating graphics... => 1441440
[6,2,2,2,1] generating graphics... => 1081080
[6,2,2,1,1,1] generating graphics... => 2162160
[6,2,1,1,1,1,1] generating graphics... => 4324320
[6,1,1,1,1,1,1,1] generating graphics... => 8648640
[5,5,3] generating graphics... => 72072
[5,5,2,1] generating graphics... => 216216
[5,5,1,1,1] generating graphics... => 432432
[5,4,4] generating graphics... => 90090
[5,4,3,1] generating graphics... => 360360
[5,4,2,2] generating graphics... => 540540
[5,4,2,1,1] generating graphics... => 1081080
[5,4,1,1,1,1] generating graphics... => 2162160
[5,3,3,2] generating graphics... => 720720
[5,3,3,1,1] generating graphics... => 1441440
[5,3,2,2,1] generating graphics... => 2162160
[5,3,2,1,1,1] generating graphics... => 4324320
[5,3,1,1,1,1,1] generating graphics... => 8648640
[5,2,2,2,2] generating graphics... => 3243240
[5,2,2,2,1,1] generating graphics... => 6486480
[4,4,4,1] generating graphics... => 450450
[4,4,3,2] generating graphics... => 900900
[4,4,3,1,1] generating graphics... => 1801800
[4,4,2,2,1] generating graphics... => 2702700
[4,4,2,1,1,1] generating graphics... => 5405400
[4,3,3,3] generating graphics... => 1201200
[4,3,3,2,1] generating graphics... => 3603600
[4,3,3,1,1,1] generating graphics... => 7207200
[4,3,2,2,2] generating graphics... => 5405400
[3,3,3,3,1] generating graphics... => 4804800
[3,3,3,2,2] generating graphics... => 7207200
[14] generating graphics... => 1
[13,1] generating graphics... => 14
[12,2] generating graphics... => 91
[12,1,1] generating graphics... => 182
[11,3] generating graphics... => 364
[11,2,1] generating graphics... => 1092
[11,1,1,1] generating graphics... => 2184
[10,4] generating graphics... => 1001
[10,3,1] generating graphics... => 4004
[10,2,2] generating graphics... => 6006
[10,2,1,1] generating graphics... => 12012
[10,1,1,1,1] generating graphics... => 24024
[9,5] generating graphics... => 2002
[9,4,1] generating graphics... => 10010
[9,3,2] generating graphics... => 20020
[9,3,1,1] generating graphics... => 40040
[9,2,2,1] generating graphics... => 60060
[9,2,1,1,1] generating graphics... => 120120
[9,1,1,1,1,1] generating graphics... => 240240
[8,6] generating graphics... => 3003
[8,5,1] generating graphics... => 18018
[8,4,2] generating graphics... => 45045
[8,4,1,1] generating graphics... => 90090
[8,3,3] generating graphics... => 60060
[8,3,2,1] generating graphics... => 180180
[8,3,1,1,1] generating graphics... => 360360
[8,2,2,2] generating graphics... => 270270
[8,2,2,1,1] generating graphics... => 540540
[8,2,1,1,1,1] generating graphics... => 1081080
[8,1,1,1,1,1,1] generating graphics... => 2162160
[7,7] generating graphics... => 3432
[7,6,1] generating graphics... => 24024
[7,5,2] generating graphics... => 72072
[7,5,1,1] generating graphics... => 144144
[7,4,3] generating graphics... => 120120
[7,4,2,1] generating graphics... => 360360
[7,4,1,1,1] generating graphics... => 720720
[7,3,3,1] generating graphics... => 480480
[7,3,2,2] generating graphics... => 720720
[7,3,2,1,1] generating graphics... => 1441440
[7,3,1,1,1,1] generating graphics... => 2882880
[7,2,2,2,1] generating graphics... => 2162160
[7,2,2,1,1,1] generating graphics... => 4324320
[7,2,1,1,1,1,1] generating graphics... => 8648640
[6,6,2] generating graphics... => 84084
[6,6,1,1] generating graphics... => 168168
[6,5,3] generating graphics... => 168168
[6,5,2,1] generating graphics... => 504504
[6,5,1,1,1] generating graphics... => 1009008
[6,4,4] generating graphics... => 210210
[6,4,3,1] generating graphics... => 840840
[6,4,2,2] generating graphics... => 1261260
[6,4,2,1,1] generating graphics... => 2522520
[6,4,1,1,1,1] generating graphics... => 5045040
[6,3,3,2] generating graphics... => 1681680
[6,3,3,1,1] generating graphics... => 3363360
[6,3,2,2,1] generating graphics... => 5045040
[6,2,2,2,2] generating graphics... => 7567560
[5,5,4] generating graphics... => 252252
[5,5,3,1] generating graphics... => 1009008
[5,5,2,2] generating graphics... => 1513512
[5,5,2,1,1] generating graphics... => 3027024
[5,5,1,1,1,1] generating graphics... => 6054048
[5,4,4,1] generating graphics... => 1261260
[5,4,3,2] generating graphics... => 2522520
[5,4,3,1,1] generating graphics... => 5045040
[5,4,2,2,1] generating graphics... => 7567560
[5,3,3,3] generating graphics... => 3363360
[4,4,4,2] generating graphics... => 3153150
[4,4,4,1,1] generating graphics... => 6306300
[4,4,3,3] generating graphics... => 4204200
[15] generating graphics... => 1
[14,1] generating graphics... => 15
[13,2] generating graphics... => 105
[13,1,1] generating graphics... => 210
[12,3] generating graphics... => 455
[12,2,1] generating graphics... => 1365
[12,1,1,1] generating graphics... => 2730
[11,4] generating graphics... => 1365
[11,3,1] generating graphics... => 5460
[11,2,2] generating graphics... => 8190
[11,2,1,1] generating graphics... => 16380
[11,1,1,1,1] generating graphics... => 32760
[10,5] generating graphics... => 3003
[10,4,1] generating graphics... => 15015
[10,3,2] generating graphics... => 30030
[10,3,1,1] generating graphics... => 60060
[10,2,2,1] generating graphics... => 90090
[10,2,1,1,1] generating graphics... => 180180
[10,1,1,1,1,1] generating graphics... => 360360
[9,6] generating graphics... => 5005
[9,5,1] generating graphics... => 30030
[9,4,2] generating graphics... => 75075
[9,4,1,1] generating graphics... => 150150
[9,3,3] generating graphics... => 100100
[9,3,2,1] generating graphics... => 300300
[9,3,1,1,1] generating graphics... => 600600
[9,2,2,2] generating graphics... => 450450
[9,2,2,1,1] generating graphics... => 900900
[9,2,1,1,1,1] generating graphics... => 1801800
[9,1,1,1,1,1,1] generating graphics... => 3603600
[8,7] generating graphics... => 6435
[8,6,1] generating graphics... => 45045
[8,5,2] generating graphics... => 135135
[8,5,1,1] generating graphics... => 270270
[8,4,3] generating graphics... => 225225
[8,4,2,1] generating graphics... => 675675
[8,4,1,1,1] generating graphics... => 1351350
[8,3,3,1] generating graphics... => 900900
[8,3,2,2] generating graphics... => 1351350
[8,3,2,1,1] generating graphics... => 2702700
[8,3,1,1,1,1] generating graphics... => 5405400
[8,2,2,2,1] generating graphics... => 4054050
[8,2,2,1,1,1] generating graphics... => 8108100
[7,7,1] generating graphics... => 51480
[7,6,2] generating graphics... => 180180
[7,6,1,1] generating graphics... => 360360
[7,5,3] generating graphics... => 360360
[7,5,2,1] generating graphics... => 1081080
[7,5,1,1,1] generating graphics... => 2162160
[7,4,4] generating graphics... => 450450
[7,4,3,1] generating graphics... => 1801800
[7,4,2,2] generating graphics... => 2702700
[7,4,2,1,1] generating graphics... => 5405400
[7,3,3,2] generating graphics... => 3603600
[7,3,3,1,1] generating graphics... => 7207200
[6,6,3] generating graphics... => 420420
[6,6,2,1] generating graphics... => 1261260
[6,6,1,1,1] generating graphics... => 2522520
[6,5,4] generating graphics... => 630630
[6,5,3,1] generating graphics... => 2522520
[6,5,2,2] generating graphics... => 3783780
[6,5,2,1,1] generating graphics... => 7567560
[6,4,4,1] generating graphics... => 3153150
[6,4,3,2] generating graphics... => 6306300
[6,3,3,3] generating graphics... => 8408400
[5,5,5] generating graphics... => 756756
[5,5,4,1] generating graphics... => 3783780
[5,5,3,2] generating graphics... => 7567560
[5,4,4,2] generating graphics... => 9459450
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Description
The multinomial of the parts of a partition.
Given an integer partition $\lambda = [\lambda_1,\ldots,\lambda_k]$, this is the multinomial
$$\binom{|\lambda|}{\lambda_1,\ldots,\lambda_k}.$$
For any integer composition $\mu$ that is a rearrangement of $\lambda$, this is the number of ordered set partitions whose list of block sizes is $\mu$.
Code
def statistic(L):
    return multinomial(list(L))
Created
Mar 25, 2013 at 10:25 by Christian Stump
Updated
Oct 29, 2017 at 20:26 by Martin Rubey