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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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* This information is distributed in the hope that it will be useful, *
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-----------------------------------------------------------------------------
Statistic identifier: St001387
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: Number of standard Young tableaux of the skew shape tracing the border of the given partition.
Let $\lambda \vdash n$ be a diagram with the given partition as shape.
Add $n$ additional boxes, one in each column $1,\dotsc,n$, and let this be $\mu$.
The statistic is the number of standard Young tableaux of skew shape $\mu/\lambda$,
which is equal to $\frac{n!}{\prod_{i} (\mu_i - \lambda_i)!}$.
For example, $\lambda=[2,1,1]$ gives $\mu = [4,2,1,1]$.
The first row in the skew shape $\mu/\lambda$ has two boxes, so the number of SYT of
shape $\mu/\lambda$ is then $4!/2 = 12$.
This statistic shows up in the study of skew specialized Macdonald polynomials,
where a type of charge statistic give rise to a $q$-analogue of the above formula.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(la):
la = Partition(la)
n = la.size()
la_t = la.conjugate()
mu = Partition([c + 1 for c in la_t] + [1]*(n-len(la_t)))
return StandardTableaux(SkewPartition([mu.conjugate(), la])).cardinality()
-----------------------------------------------------------------------------
Statistic values:
[] => 1
[1] => 1
[2] => 1
[1,1] => 2
[3] => 1
[2,1] => 6
[1,1,1] => 3
[4] => 1
[3,1] => 12
[2,2] => 6
[2,1,1] => 12
[1,1,1,1] => 4
[5] => 1
[4,1] => 20
[3,2] => 30
[3,1,1] => 30
[2,2,1] => 20
[2,1,1,1] => 20
[1,1,1,1,1] => 5
[6] => 1
[5,1] => 30
[4,2] => 90
[4,1,1] => 60
[3,3] => 20
[3,2,1] => 120
[3,1,1,1] => 60
[2,2,2] => 15
[2,2,1,1] => 30
[2,1,1,1,1] => 30
[1,1,1,1,1,1] => 6
[7] => 1
[6,1] => 42
[5,2] => 210
[5,1,1] => 105
[4,3] => 140
[4,2,1] => 420
[4,1,1,1] => 140
[3,3,1] => 105
[3,2,2] => 105
[3,2,1,1] => 210
[3,1,1,1,1] => 105
[2,2,2,1] => 42
[2,2,1,1,1] => 42
[2,1,1,1,1,1] => 42
[1,1,1,1,1,1,1] => 7
[8] => 1
[7,1] => 56
[6,2] => 420
[6,1,1] => 168
[5,3] => 560
[5,2,1] => 1120
[5,1,1,1] => 280
[4,4] => 70
[4,3,1] => 840
[4,2,2] => 420
[4,2,1,1] => 840
[4,1,1,1,1] => 280
[3,3,2] => 168
[3,3,1,1] => 168
[3,2,2,1] => 336
[3,2,1,1,1] => 336
[3,1,1,1,1,1] => 168
[2,2,2,2] => 28
[2,2,2,1,1] => 56
[2,2,1,1,1,1] => 56
[2,1,1,1,1,1,1] => 56
[1,1,1,1,1,1,1,1] => 8
[9] => 1
[8,1] => 72
[7,2] => 756
[7,1,1] => 252
[6,3] => 1680
[6,2,1] => 2520
[6,1,1,1] => 504
[5,4] => 630
[5,3,1] => 3780
[5,2,2] => 1260
[5,2,1,1] => 2520
[5,1,1,1,1] => 630
[4,4,1] => 504
[4,3,2] => 1512
[4,3,1,1] => 1512
[4,2,2,1] => 1512
[4,2,1,1,1] => 1512
[4,1,1,1,1,1] => 504
[3,3,3] => 84
[3,3,2,1] => 504
[3,3,1,1,1] => 252
[3,2,2,2] => 252
[3,2,2,1,1] => 504
[3,2,1,1,1,1] => 504
[3,1,1,1,1,1,1] => 252
[2,2,2,2,1] => 72
[2,2,2,1,1,1] => 72
[2,2,1,1,1,1,1] => 72
[2,1,1,1,1,1,1,1] => 72
[1,1,1,1,1,1,1,1,1] => 9
[10] => 1
[9,1] => 90
[8,2] => 1260
[8,1,1] => 360
[7,3] => 4200
[7,2,1] => 5040
[7,1,1,1] => 840
[6,4] => 3150
[6,3,1] => 12600
[6,2,2] => 3150
[6,2,1,1] => 6300
[6,1,1,1,1] => 1260
[5,5] => 252
[5,4,1] => 5040
[5,3,2] => 7560
[5,3,1,1] => 7560
[5,2,2,1] => 5040
[5,2,1,1,1] => 5040
[5,1,1,1,1,1] => 1260
[4,4,2] => 1260
[4,4,1,1] => 840
[4,3,3] => 840
[4,3,2,1] => 5040
[4,3,1,1,1] => 2520
[4,2,2,2] => 1260
[4,2,2,1,1] => 2520
[4,2,1,1,1,1] => 2520
[4,1,1,1,1,1,1] => 840
[3,3,3,1] => 360
[3,3,2,2] => 360
[3,3,2,1,1] => 720
[3,3,1,1,1,1] => 360
[3,2,2,2,1] => 720
[3,2,2,1,1,1] => 720
[3,2,1,1,1,1,1] => 720
[3,1,1,1,1,1,1,1] => 360
[2,2,2,2,2] => 45
[2,2,2,2,1,1] => 90
[2,2,2,1,1,1,1] => 90
[2,2,1,1,1,1,1,1] => 90
[2,1,1,1,1,1,1,1,1] => 90
[1,1,1,1,1,1,1,1,1,1] => 10
[11] => 1
[10,1] => 110
[9,2] => 1980
[9,1,1] => 495
[8,3] => 9240
[8,2,1] => 9240
[8,1,1,1] => 1320
[7,4] => 11550
[7,3,1] => 34650
[7,2,2] => 6930
[7,2,1,1] => 13860
[7,1,1,1,1] => 2310
[6,5] => 2772
[6,4,1] => 27720
[6,3,2] => 27720
[6,3,1,1] => 27720
[6,2,2,1] => 13860
[6,2,1,1,1] => 13860
[6,1,1,1,1,1] => 2772
[5,5,1] => 2310
[5,4,2] => 13860
[5,4,1,1] => 9240
[5,3,3] => 4620
[5,3,2,1] => 27720
[5,3,1,1,1] => 13860
[5,2,2,2] => 4620
[5,2,2,1,1] => 9240
[5,2,1,1,1,1] => 9240
[5,1,1,1,1,1,1] => 2310
[4,4,3] => 1320
[4,4,2,1] => 3960
[4,4,1,1,1] => 1320
[4,3,3,1] => 3960
[4,3,2,2] => 3960
[4,3,2,1,1] => 7920
[4,3,1,1,1,1] => 3960
[4,2,2,2,1] => 3960
[4,2,2,1,1,1] => 3960
[4,2,1,1,1,1,1] => 3960
[4,1,1,1,1,1,1,1] => 1320
[3,3,3,2] => 495
[3,3,3,1,1] => 495
[3,3,2,2,1] => 990
[3,3,2,1,1,1] => 990
[3,3,1,1,1,1,1] => 495
[3,2,2,2,2] => 495
[3,2,2,2,1,1] => 990
[3,2,2,1,1,1,1] => 990
[3,2,1,1,1,1,1,1] => 990
[3,1,1,1,1,1,1,1,1] => 495
[2,2,2,2,2,1] => 110
[2,2,2,2,1,1,1] => 110
[2,2,2,1,1,1,1,1] => 110
[2,2,1,1,1,1,1,1,1] => 110
[2,1,1,1,1,1,1,1,1,1] => 110
[1,1,1,1,1,1,1,1,1,1,1] => 11
[12] => 1
[11,1] => 132
[10,2] => 2970
[10,1,1] => 660
[9,3] => 18480
[9,2,1] => 15840
[9,1,1,1] => 1980
[8,4] => 34650
[8,3,1] => 83160
[8,2,2] => 13860
[8,2,1,1] => 27720
[8,1,1,1,1] => 3960
[7,5] => 16632
[7,4,1] => 110880
[7,3,2] => 83160
[7,3,1,1] => 83160
[7,2,2,1] => 33264
[7,2,1,1,1] => 33264
[7,1,1,1,1,1] => 5544
[6,6] => 924
[6,5,1] => 27720
[6,4,2] => 83160
[6,4,1,1] => 55440
[6,3,3] => 18480
[6,3,2,1] => 110880
[6,3,1,1,1] => 55440
[6,2,2,2] => 13860
[6,2,2,1,1] => 27720
[6,2,1,1,1,1] => 27720
[6,1,1,1,1,1,1] => 5544
[5,5,2] => 7920
[5,5,1,1] => 3960
[5,4,3] => 15840
[5,4,2,1] => 47520
[5,4,1,1,1] => 15840
[5,3,3,1] => 23760
[5,3,2,2] => 23760
[5,3,2,1,1] => 47520
[5,3,1,1,1,1] => 23760
[5,2,2,2,1] => 15840
[5,2,2,1,1,1] => 15840
[5,2,1,1,1,1,1] => 15840
[5,1,1,1,1,1,1,1] => 3960
[4,4,4] => 495
[4,4,3,1] => 5940
[4,4,2,2] => 2970
[4,4,2,1,1] => 5940
[4,4,1,1,1,1] => 1980
[4,3,3,2] => 5940
[4,3,3,1,1] => 5940
[4,3,2,2,1] => 11880
[4,3,2,1,1,1] => 11880
[4,3,1,1,1,1,1] => 5940
[4,2,2,2,2] => 2970
[4,2,2,2,1,1] => 5940
[4,2,2,1,1,1,1] => 5940
[4,2,1,1,1,1,1,1] => 5940
[4,1,1,1,1,1,1,1,1] => 1980
[3,3,3,3] => 220
[3,3,3,2,1] => 1320
[3,3,3,1,1,1] => 660
[3,3,2,2,2] => 660
[3,3,2,2,1,1] => 1320
[3,3,2,1,1,1,1] => 1320
[3,3,1,1,1,1,1,1] => 660
[3,2,2,2,2,1] => 1320
[3,2,2,2,1,1,1] => 1320
[3,2,2,1,1,1,1,1] => 1320
[3,2,1,1,1,1,1,1,1] => 1320
[3,1,1,1,1,1,1,1,1,1] => 660
[2,2,2,2,2,2] => 66
[2,2,2,2,2,1,1] => 132
[2,2,2,2,1,1,1,1] => 132
[2,2,2,1,1,1,1,1,1] => 132
[2,2,1,1,1,1,1,1,1,1] => 132
[2,1,1,1,1,1,1,1,1,1,1] => 132
[1,1,1,1,1,1,1,1,1,1,1,1] => 12
[13] => 1
[12,1] => 156
[11,2] => 4290
[11,1,1] => 858
[10,3] => 34320
[10,2,1] => 25740
[10,1,1,1] => 2860
[9,4] => 90090
[9,3,1] => 180180
[9,2,2] => 25740
[9,2,1,1] => 51480
[9,1,1,1,1] => 6435
[8,5] => 72072
[8,4,1] => 360360
[8,3,2] => 216216
[8,3,1,1] => 216216
[8,2,2,1] => 72072
[8,2,1,1,1] => 72072
[8,1,1,1,1,1] => 10296
[7,6] => 12012
[7,5,1] => 180180
[7,4,2] => 360360
[7,4,1,1] => 240240
[7,3,3] => 60060
[7,3,2,1] => 360360
[7,3,1,1,1] => 180180
[7,2,2,2] => 36036
[7,2,2,1,1] => 72072
[7,2,1,1,1,1] => 72072
[7,1,1,1,1,1,1] => 12012
[6,6,1] => 10296
[6,5,2] => 102960
[6,5,1,1] => 51480
[6,4,3] => 102960
[6,4,2,1] => 308880
[6,4,1,1,1] => 102960
[6,3,3,1] => 102960
[6,3,2,2] => 102960
[6,3,2,1,1] => 205920
[6,3,1,1,1,1] => 102960
[6,2,2,2,1] => 51480
[6,2,2,1,1,1] => 51480
[6,2,1,1,1,1,1] => 51480
[6,1,1,1,1,1,1,1] => 10296
[5,5,3] => 12870
[5,5,2,1] => 25740
[5,5,1,1,1] => 6435
[5,4,4] => 6435
[5,4,3,1] => 77220
[5,4,2,2] => 38610
[5,4,2,1,1] => 77220
[5,4,1,1,1,1] => 25740
[5,3,3,2] => 38610
[5,3,3,1,1] => 38610
[5,3,2,2,1] => 77220
[5,3,2,1,1,1] => 77220
[5,3,1,1,1,1,1] => 38610
[5,2,2,2,2] => 12870
[5,2,2,2,1,1] => 25740
[5,2,2,1,1,1,1] => 25740
[5,2,1,1,1,1,1,1] => 25740
[5,1,1,1,1,1,1,1,1] => 6435
[4,4,4,1] => 2860
[4,4,3,2] => 8580
[4,4,3,1,1] => 8580
[4,4,2,2,1] => 8580
[4,4,2,1,1,1] => 8580
[4,4,1,1,1,1,1] => 2860
[4,3,3,3] => 2860
[4,3,3,2,1] => 17160
[4,3,3,1,1,1] => 8580
[4,3,2,2,2] => 8580
[4,3,2,2,1,1] => 17160
[4,3,2,1,1,1,1] => 17160
[4,3,1,1,1,1,1,1] => 8580
[4,2,2,2,2,1] => 8580
[4,2,2,2,1,1,1] => 8580
[4,2,2,1,1,1,1,1] => 8580
[4,2,1,1,1,1,1,1,1] => 8580
[4,1,1,1,1,1,1,1,1,1] => 2860
[3,3,3,3,1] => 858
[3,3,3,2,2] => 858
[3,3,3,2,1,1] => 1716
[3,3,3,1,1,1,1] => 858
[3,3,2,2,2,1] => 1716
[3,3,2,2,1,1,1] => 1716
[3,3,2,1,1,1,1,1] => 1716
[3,3,1,1,1,1,1,1,1] => 858
[3,2,2,2,2,2] => 858
[3,2,2,2,2,1,1] => 1716
[3,2,2,2,1,1,1,1] => 1716
[3,2,2,1,1,1,1,1,1] => 1716
[3,2,1,1,1,1,1,1,1,1] => 1716
[3,1,1,1,1,1,1,1,1,1,1] => 858
[2,2,2,2,2,2,1] => 156
[2,2,2,2,2,1,1,1] => 156
[2,2,2,2,1,1,1,1,1] => 156
[2,2,2,1,1,1,1,1,1,1] => 156
[2,2,1,1,1,1,1,1,1,1,1] => 156
[2,1,1,1,1,1,1,1,1,1,1,1] => 156
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 13
[14] => 1
[13,1] => 182
[12,2] => 6006
[12,1,1] => 1092
[11,3] => 60060
[11,2,1] => 40040
[11,1,1,1] => 4004
[10,4] => 210210
[10,3,1] => 360360
[10,2,2] => 45045
[10,2,1,1] => 90090
[10,1,1,1,1] => 10010
[9,5] => 252252
[9,4,1] => 1009008
[9,3,2] => 504504
[9,3,1,1] => 504504
[9,2,2,1] => 144144
[9,2,1,1,1] => 144144
[9,1,1,1,1,1] => 18018
[8,6] => 84084
[8,5,1] => 840840
[8,4,2] => 1261260
[8,4,1,1] => 840840
[8,3,3] => 168168
[8,3,2,1] => 1009008
[8,3,1,1,1] => 504504
[8,2,2,2] => 84084
[8,2,2,1,1] => 168168
[8,2,1,1,1,1] => 168168
[8,1,1,1,1,1,1] => 24024
[7,7] => 3432
[7,6,1] => 144144
[7,5,2] => 720720
[7,5,1,1] => 360360
[7,4,3] => 480480
[7,4,2,1] => 1441440
[7,4,1,1,1] => 480480
[7,3,3,1] => 360360
[7,3,2,2] => 360360
[7,3,2,1,1] => 720720
[7,3,1,1,1,1] => 360360
[7,2,2,2,1] => 144144
[7,2,2,1,1,1] => 144144
[7,2,1,1,1,1,1] => 144144
[7,1,1,1,1,1,1,1] => 24024
[6,6,2] => 45045
[6,6,1,1] => 18018
[6,5,3] => 180180
[6,5,2,1] => 360360
[6,5,1,1,1] => 90090
[6,4,4] => 45045
[6,4,3,1] => 540540
[6,4,2,2] => 270270
[6,4,2,1,1] => 540540
[6,4,1,1,1,1] => 180180
[6,3,3,2] => 180180
[6,3,3,1,1] => 180180
[6,3,2,2,1] => 360360
[6,3,2,1,1,1] => 360360
[6,3,1,1,1,1,1] => 180180
[6,2,2,2,2] => 45045
[6,2,2,2,1,1] => 90090
[6,2,2,1,1,1,1] => 90090
[6,2,1,1,1,1,1,1] => 90090
[6,1,1,1,1,1,1,1,1] => 18018
[5,5,4] => 10010
[5,5,3,1] => 60060
[5,5,2,2] => 20020
[5,5,2,1,1] => 40040
[5,5,1,1,1,1] => 10010
[5,4,4,1] => 40040
[5,4,3,2] => 120120
[5,4,3,1,1] => 120120
[5,4,2,2,1] => 120120
[5,4,2,1,1,1] => 120120
[5,4,1,1,1,1,1] => 40040
[5,3,3,3] => 20020
[5,3,3,2,1] => 120120
[5,3,3,1,1,1] => 60060
[5,3,2,2,2] => 60060
[5,3,2,2,1,1] => 120120
[5,3,2,1,1,1,1] => 120120
[5,3,1,1,1,1,1,1] => 60060
[5,2,2,2,2,1] => 40040
[5,2,2,2,1,1,1] => 40040
[5,2,2,1,1,1,1,1] => 40040
[5,2,1,1,1,1,1,1,1] => 40040
[5,1,1,1,1,1,1,1,1,1] => 10010
[4,4,4,2] => 6006
[4,4,4,1,1] => 4004
[4,4,3,3] => 4004
[4,4,3,2,1] => 24024
[4,4,3,1,1,1] => 12012
[4,4,2,2,2] => 6006
[4,4,2,2,1,1] => 12012
[4,4,2,1,1,1,1] => 12012
[4,4,1,1,1,1,1,1] => 4004
[4,3,3,3,1] => 12012
[4,3,3,2,2] => 12012
[4,3,3,2,1,1] => 24024
[4,3,3,1,1,1,1] => 12012
[4,3,2,2,2,1] => 24024
[4,3,2,2,1,1,1] => 24024
[4,3,2,1,1,1,1,1] => 24024
[4,3,1,1,1,1,1,1,1] => 12012
[4,2,2,2,2,2] => 6006
[4,2,2,2,2,1,1] => 12012
[4,2,2,2,1,1,1,1] => 12012
[4,2,2,1,1,1,1,1,1] => 12012
[4,2,1,1,1,1,1,1,1,1] => 12012
[4,1,1,1,1,1,1,1,1,1,1] => 4004
[3,3,3,3,2] => 1092
[3,3,3,3,1,1] => 1092
[3,3,3,2,2,1] => 2184
[3,3,3,2,1,1,1] => 2184
[3,3,3,1,1,1,1,1] => 1092
[3,3,2,2,2,2] => 1092
[3,3,2,2,2,1,1] => 2184
[3,3,2,2,1,1,1,1] => 2184
[3,3,2,1,1,1,1,1,1] => 2184
[3,3,1,1,1,1,1,1,1,1] => 1092
[3,2,2,2,2,2,1] => 2184
[3,2,2,2,2,1,1,1] => 2184
[3,2,2,2,1,1,1,1,1] => 2184
[3,2,2,1,1,1,1,1,1,1] => 2184
[3,2,1,1,1,1,1,1,1,1,1] => 2184
[3,1,1,1,1,1,1,1,1,1,1,1] => 1092
[2,2,2,2,2,2,2] => 91
[2,2,2,2,2,2,1,1] => 182
[2,2,2,2,2,1,1,1,1] => 182
[2,2,2,2,1,1,1,1,1,1] => 182
[2,2,2,1,1,1,1,1,1,1,1] => 182
[2,2,1,1,1,1,1,1,1,1,1,1] => 182
[2,1,1,1,1,1,1,1,1,1,1,1,1] => 182
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 14
[15] => 1
[14,1] => 210
[13,2] => 8190
[13,1,1] => 1365
[12,3] => 100100
[12,2,1] => 60060
[12,1,1,1] => 5460
[11,4] => 450450
[11,3,1] => 675675
[11,2,2] => 75075
[11,2,1,1] => 150150
[11,1,1,1,1] => 15015
[10,5] => 756756
[10,4,1] => 2522520
[10,3,2] => 1081080
[10,3,1,1] => 1081080
[10,2,2,1] => 270270
[10,2,1,1,1] => 270270
[10,1,1,1,1,1] => 30030
[9,6] => 420420
[9,5,1] => 3153150
[9,4,2] => 3783780
[9,4,1,1] => 2522520
[9,3,3] => 420420
[9,3,2,1] => 2522520
[9,3,1,1,1] => 1261260
[9,2,2,2] => 180180
[9,2,2,1,1] => 360360
[9,2,1,1,1,1] => 360360
[9,1,1,1,1,1,1] => 45045
[8,7] => 51480
[8,6,1] => 1081080
[8,5,2] => 3603600
[8,5,1,1] => 1801800
[8,4,3] => 1801800
[8,4,2,1] => 5405400
[8,4,1,1,1] => 1801800
[8,3,3,1] => 1081080
[8,3,2,2] => 1081080
[8,3,2,1,1] => 2162160
[8,3,1,1,1,1] => 1081080
[8,2,2,2,1] => 360360
[8,2,2,1,1,1] => 360360
[8,2,1,1,1,1,1] => 360360
[8,1,1,1,1,1,1,1] => 51480
[7,7,1] => 45045
[7,6,2] => 675675
[7,6,1,1] => 270270
[7,5,3] => 1351350
[7,5,2,1] => 2702700
[7,5,1,1,1] => 675675
[7,4,4] => 225225
[7,4,3,1] => 2702700
[7,4,2,2] => 1351350
[7,4,2,1,1] => 2702700
[7,4,1,1,1,1] => 900900
[7,3,3,2] => 675675
[7,3,3,1,1] => 675675
[7,3,2,2,1] => 1351350
[7,3,2,1,1,1] => 1351350
[7,3,1,1,1,1,1] => 675675
[7,2,2,2,2] => 135135
[7,2,2,2,1,1] => 270270
[7,2,2,1,1,1,1] => 270270
[7,2,1,1,1,1,1,1] => 270270
[7,1,1,1,1,1,1,1,1] => 45045
[6,6,3] => 100100
[6,6,2,1] => 150150
[6,6,1,1,1] => 30030
[6,5,4] => 150150
[6,5,3,1] => 900900
[6,5,2,2] => 300300
[6,5,2,1,1] => 600600
[6,5,1,1,1,1] => 150150
[6,4,4,1] => 300300
[6,4,3,2] => 900900
[6,4,3,1,1] => 900900
[6,4,2,2,1] => 900900
[6,4,2,1,1,1] => 900900
[6,4,1,1,1,1,1] => 300300
[6,3,3,3] => 100100
[6,3,3,2,1] => 600600
[6,3,3,1,1,1] => 300300
[6,3,2,2,2] => 300300
[6,3,2,2,1,1] => 600600
[6,3,2,1,1,1,1] => 600600
[6,3,1,1,1,1,1,1] => 300300
[6,2,2,2,2,1] => 150150
[6,2,2,2,1,1,1] => 150150
[6,2,2,1,1,1,1,1] => 150150
[6,2,1,1,1,1,1,1,1] => 150150
[6,1,1,1,1,1,1,1,1,1] => 30030
[5,5,5] => 3003
[5,5,4,1] => 60060
[5,5,3,2] => 90090
[5,5,3,1,1] => 90090
[5,5,2,2,1] => 60060
[5,5,2,1,1,1] => 60060
[5,5,1,1,1,1,1] => 15015
[5,4,4,2] => 90090
[5,4,4,1,1] => 60060
[5,4,3,3] => 60060
[5,4,3,2,1] => 360360
[5,4,3,1,1,1] => 180180
[5,4,2,2,2] => 90090
[5,4,2,2,1,1] => 180180
[5,4,2,1,1,1,1] => 180180
[5,4,1,1,1,1,1,1] => 60060
[5,3,3,3,1] => 90090
[5,3,3,2,2] => 90090
[5,3,3,2,1,1] => 180180
[5,3,3,1,1,1,1] => 90090
[5,3,2,2,2,1] => 180180
[5,3,2,2,1,1,1] => 180180
[5,3,2,1,1,1,1,1] => 180180
[5,3,1,1,1,1,1,1,1] => 90090
[5,2,2,2,2,2] => 30030
[5,2,2,2,2,1,1] => 60060
[5,2,2,2,1,1,1,1] => 60060
[5,2,2,1,1,1,1,1,1] => 60060
[5,2,1,1,1,1,1,1,1,1] => 60060
[5,1,1,1,1,1,1,1,1,1,1] => 15015
[4,4,4,3] => 5460
[4,4,4,2,1] => 16380
[4,4,4,1,1,1] => 5460
[4,4,3,3,1] => 16380
[4,4,3,2,2] => 16380
[4,4,3,2,1,1] => 32760
[4,4,3,1,1,1,1] => 16380
[4,4,2,2,2,1] => 16380
[4,4,2,2,1,1,1] => 16380
[4,4,2,1,1,1,1,1] => 16380
[4,4,1,1,1,1,1,1,1] => 5460
[4,3,3,3,2] => 16380
[4,3,3,3,1,1] => 16380
[4,3,3,2,2,1] => 32760
[4,3,3,2,1,1,1] => 32760
[4,3,3,1,1,1,1,1] => 16380
[4,3,2,2,2,2] => 16380
[4,3,2,2,2,1,1] => 32760
[4,3,2,2,1,1,1,1] => 32760
[4,3,2,1,1,1,1,1,1] => 32760
[4,3,1,1,1,1,1,1,1,1] => 16380
[4,2,2,2,2,2,1] => 16380
[4,2,2,2,2,1,1,1] => 16380
[4,2,2,2,1,1,1,1,1] => 16380
[4,2,2,1,1,1,1,1,1,1] => 16380
[4,2,1,1,1,1,1,1,1,1,1] => 16380
[4,1,1,1,1,1,1,1,1,1,1,1] => 5460
[3,3,3,3,3] => 455
[3,3,3,3,2,1] => 2730
[3,3,3,3,1,1,1] => 1365
[3,3,3,2,2,2] => 1365
[3,3,3,2,2,1,1] => 2730
[3,3,3,2,1,1,1,1] => 2730
[3,3,3,1,1,1,1,1,1] => 1365
[3,3,2,2,2,2,1] => 2730
[3,3,2,2,2,1,1,1] => 2730
[3,3,2,2,1,1,1,1,1] => 2730
[3,3,2,1,1,1,1,1,1,1] => 2730
[3,3,1,1,1,1,1,1,1,1,1] => 1365
[3,2,2,2,2,2,2] => 1365
[3,2,2,2,2,2,1,1] => 2730
[3,2,2,2,2,1,1,1,1] => 2730
[3,2,2,2,1,1,1,1,1,1] => 2730
[3,2,2,1,1,1,1,1,1,1,1] => 2730
[3,2,1,1,1,1,1,1,1,1,1,1] => 2730
[3,1,1,1,1,1,1,1,1,1,1,1,1] => 1365
[2,2,2,2,2,2,2,1] => 210
[2,2,2,2,2,2,1,1,1] => 210
[2,2,2,2,2,1,1,1,1,1] => 210
[2,2,2,2,1,1,1,1,1,1,1] => 210
[2,2,2,1,1,1,1,1,1,1,1,1] => 210
[2,2,1,1,1,1,1,1,1,1,1,1,1] => 210
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 210
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 15
[16] => 1
[15,1] => 240
[14,2] => 10920
[14,1,1] => 1680
[13,3] => 160160
[13,2,1] => 87360
[13,1,1,1] => 7280
[12,4] => 900900
[12,3,1] => 1201200
[12,2,2] => 120120
[12,2,1,1] => 240240
[12,1,1,1,1] => 21840
[11,5] => 2018016
[11,4,1] => 5765760
[11,3,2] => 2162160
[11,3,1,1] => 2162160
[11,2,2,1] => 480480
[11,2,1,1,1] => 480480
[11,1,1,1,1,1] => 48048
[10,6] => 1681680
[10,5,1] => 10090080
[10,4,2] => 10090080
[10,4,1,1] => 6726720
[10,3,3] => 960960
[10,3,2,1] => 5765760
[10,3,1,1,1] => 2882880
[10,2,2,2] => 360360
[10,2,2,1,1] => 720720
[10,2,1,1,1,1] => 720720
[10,1,1,1,1,1,1] => 80080
[9,7] => 411840
[9,6,1] => 5765760
[9,5,2] => 14414400
[9,5,1,1] => 7207200
[9,4,3] => 5765760
[9,4,2,1] => 17297280
[9,4,1,1,1] => 5765760
[9,3,3,1] => 2882880
[9,3,2,2] => 2882880
[9,3,2,1,1] => 5765760
[9,3,1,1,1,1] => 2882880
[9,2,2,2,1] => 823680
[9,2,2,1,1,1] => 823680
[9,2,1,1,1,1,1] => 823680
[9,1,1,1,1,1,1,1] => 102960
[8,8] => 12870
[8,7,1] => 720720
[8,6,2] => 5405400
[8,6,1,1] => 2162160
[8,5,3] => 7207200
[8,5,2,1] => 14414400
[8,5,1,1,1] => 3603600
[8,4,4] => 900900
[8,4,3,1] => 10810800
[8,4,2,2] => 5405400
[8,4,2,1,1] => 10810800
[8,4,1,1,1,1] => 3603600
[8,3,3,2] => 2162160
[8,3,3,1,1] => 2162160
[8,3,2,2,1] => 4324320
[8,3,2,1,1,1] => 4324320
[8,3,1,1,1,1,1] => 2162160
[8,2,2,2,2] => 360360
[8,2,2,2,1,1] => 720720
[8,2,2,1,1,1,1] => 720720
[8,2,1,1,1,1,1,1] => 720720
[8,1,1,1,1,1,1,1,1] => 102960
[7,7,2] => 240240
[7,7,1,1] => 80080
[7,6,3] => 1601600
[7,6,2,1] => 2402400
[7,6,1,1,1] => 480480
[7,5,4] => 1201200
[7,5,3,1] => 7207200
[7,5,2,2] => 2402400
[7,5,2,1,1] => 4804800
[7,5,1,1,1,1] => 1201200
[7,4,4,1] => 1601600
[7,4,3,2] => 4804800
[7,4,3,1,1] => 4804800
[7,4,2,2,1] => 4804800
[7,4,2,1,1,1] => 4804800
[7,4,1,1,1,1,1] => 1601600
[7,3,3,3] => 400400
[7,3,3,2,1] => 2402400
[7,3,3,1,1,1] => 1201200
[7,3,2,2,2] => 1201200
[7,3,2,2,1,1] => 2402400
[7,3,2,1,1,1,1] => 2402400
[7,3,1,1,1,1,1,1] => 1201200
[7,2,2,2,2,1] => 480480
[7,2,2,2,1,1,1] => 480480
[7,2,2,1,1,1,1,1] => 480480
[7,2,1,1,1,1,1,1,1] => 480480
[7,1,1,1,1,1,1,1,1,1] => 80080
[6,6,4] => 120120
[6,6,3,1] => 480480
[6,6,2,2] => 120120
[6,6,2,1,1] => 240240
[6,6,1,1,1,1] => 48048
[6,5,5] => 48048
[6,5,4,1] => 960960
[6,5,3,2] => 1441440
[6,5,3,1,1] => 1441440
[6,5,2,2,1] => 960960
[6,5,2,1,1,1] => 960960
[6,5,1,1,1,1,1] => 240240
[6,4,4,2] => 720720
[6,4,4,1,1] => 480480
[6,4,3,3] => 480480
[6,4,3,2,1] => 2882880
[6,4,3,1,1,1] => 1441440
[6,4,2,2,2] => 720720
[6,4,2,2,1,1] => 1441440
[6,4,2,1,1,1,1] => 1441440
[6,4,1,1,1,1,1,1] => 480480
[6,3,3,3,1] => 480480
[6,3,3,2,2] => 480480
[6,3,3,2,1,1] => 960960
[6,3,3,1,1,1,1] => 480480
[6,3,2,2,2,1] => 960960
[6,3,2,2,1,1,1] => 960960
[6,3,2,1,1,1,1,1] => 960960
[6,3,1,1,1,1,1,1,1] => 480480
[6,2,2,2,2,2] => 120120
[6,2,2,2,2,1,1] => 240240
[6,2,2,2,1,1,1,1] => 240240
[6,2,2,1,1,1,1,1,1] => 240240
[6,2,1,1,1,1,1,1,1,1] => 240240
[6,1,1,1,1,1,1,1,1,1,1] => 48048
[5,5,5,1] => 21840
[5,5,4,2] => 131040
[5,5,4,1,1] => 87360
[5,5,3,3] => 43680
[5,5,3,2,1] => 262080
[5,5,3,1,1,1] => 131040
[5,5,2,2,2] => 43680
[5,5,2,2,1,1] => 87360
[5,5,2,1,1,1,1] => 87360
[5,5,1,1,1,1,1,1] => 21840
[5,4,4,3] => 87360
[5,4,4,2,1] => 262080
[5,4,4,1,1,1] => 87360
[5,4,3,3,1] => 262080
[5,4,3,2,2] => 262080
[5,4,3,2,1,1] => 524160
[5,4,3,1,1,1,1] => 262080
[5,4,2,2,2,1] => 262080
[5,4,2,2,1,1,1] => 262080
[5,4,2,1,1,1,1,1] => 262080
[5,4,1,1,1,1,1,1,1] => 87360
[5,3,3,3,2] => 131040
[5,3,3,3,1,1] => 131040
[5,3,3,2,2,1] => 262080
[5,3,3,2,1,1,1] => 262080
[5,3,3,1,1,1,1,1] => 131040
[5,3,2,2,2,2] => 131040
[5,3,2,2,2,1,1] => 262080
[5,3,2,2,1,1,1,1] => 262080
[5,3,2,1,1,1,1,1,1] => 262080
[5,3,1,1,1,1,1,1,1,1] => 131040
[5,2,2,2,2,2,1] => 87360
[5,2,2,2,2,1,1,1] => 87360
[5,2,2,2,1,1,1,1,1] => 87360
[5,2,2,1,1,1,1,1,1,1] => 87360
[5,2,1,1,1,1,1,1,1,1,1] => 87360
[5,1,1,1,1,1,1,1,1,1,1,1] => 21840
[4,4,4,4] => 1820
[4,4,4,3,1] => 21840
[4,4,4,2,2] => 10920
[4,4,4,2,1,1] => 21840
[4,4,4,1,1,1,1] => 7280
[4,4,3,3,2] => 21840
[4,4,3,3,1,1] => 21840
[4,4,3,2,2,1] => 43680
[4,4,3,2,1,1,1] => 43680
[4,4,3,1,1,1,1,1] => 21840
[4,4,2,2,2,2] => 10920
[4,4,2,2,2,1,1] => 21840
[4,4,2,2,1,1,1,1] => 21840
[4,4,2,1,1,1,1,1,1] => 21840
[4,4,1,1,1,1,1,1,1,1] => 7280
[4,3,3,3,3] => 7280
[4,3,3,3,2,1] => 43680
[4,3,3,3,1,1,1] => 21840
[4,3,3,2,2,2] => 21840
[4,3,3,2,2,1,1] => 43680
[4,3,3,2,1,1,1,1] => 43680
[4,3,3,1,1,1,1,1,1] => 21840
[4,3,2,2,2,2,1] => 43680
[4,3,2,2,2,1,1,1] => 43680
[4,3,2,2,1,1,1,1,1] => 43680
[4,3,2,1,1,1,1,1,1,1] => 43680
[4,3,1,1,1,1,1,1,1,1,1] => 21840
[4,2,2,2,2,2,2] => 10920
[4,2,2,2,2,2,1,1] => 21840
[4,2,2,2,2,1,1,1,1] => 21840
[4,2,2,2,1,1,1,1,1,1] => 21840
[4,2,2,1,1,1,1,1,1,1,1] => 21840
[4,2,1,1,1,1,1,1,1,1,1,1] => 21840
[4,1,1,1,1,1,1,1,1,1,1,1,1] => 7280
[3,3,3,3,3,1] => 1680
[3,3,3,3,2,2] => 1680
[3,3,3,3,2,1,1] => 3360
[3,3,3,3,1,1,1,1] => 1680
[3,3,3,2,2,2,1] => 3360
[3,3,3,2,2,1,1,1] => 3360
[3,3,3,2,1,1,1,1,1] => 3360
[3,3,3,1,1,1,1,1,1,1] => 1680
[3,3,2,2,2,2,2] => 1680
[3,3,2,2,2,2,1,1] => 3360
[3,3,2,2,2,1,1,1,1] => 3360
[3,3,2,2,1,1,1,1,1,1] => 3360
[3,3,2,1,1,1,1,1,1,1,1] => 3360
[3,3,1,1,1,1,1,1,1,1,1,1] => 1680
[3,2,2,2,2,2,2,1] => 3360
[3,2,2,2,2,2,1,1,1] => 3360
[3,2,2,2,2,1,1,1,1,1] => 3360
[3,2,2,2,1,1,1,1,1,1,1] => 3360
[3,2,2,1,1,1,1,1,1,1,1,1] => 3360
[3,2,1,1,1,1,1,1,1,1,1,1,1] => 3360
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1680
[2,2,2,2,2,2,2,2] => 120
[2,2,2,2,2,2,2,1,1] => 240
[2,2,2,2,2,2,1,1,1,1] => 240
[2,2,2,2,2,1,1,1,1,1,1] => 240
[2,2,2,2,1,1,1,1,1,1,1,1] => 240
[2,2,2,1,1,1,1,1,1,1,1,1,1] => 240
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 240
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 240
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 16
-----------------------------------------------------------------------------
Created: Apr 30, 2019 at 11:28 by Per Alexandersson
-----------------------------------------------------------------------------
Last Updated: Apr 23, 2022 at 10:56 by Martin Rubey