- FindStat

Identifier

St000817: Integer compositions ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1,1]=>1
[2]=>2
[1,1,1]=>1
[1,2]=>2
[2,1]=>4
[3]=>4
[1,1,1,1]=>1
[1,1,2]=>2
[1,2,1]=>4
[1,3]=>4
[2,1,1]=>6
[2,2]=>10
[3,1]=>12
[4]=>8
[1,1,1,1,1]=>1
[1,1,1,2]=>2
[1,1,2,1]=>4
[1,1,3]=>4
[1,2,1,1]=>6
[1,2,2]=>10
[1,3,1]=>12
[1,4]=>8
[2,1,1,1]=>8
[2,1,2]=>14
[2,2,1]=>28
[2,3]=>24
[3,1,1]=>24
[3,2]=>36
[4,1]=>32
[5]=>16
[1,1,1,1,1,1]=>1
[1,1,1,1,2]=>2
[1,1,1,2,1]=>4
[1,1,1,3]=>4
[1,1,2,1,1]=>6
[1,1,2,2]=>10
[1,1,3,1]=>12
[1,1,4]=>8
[1,2,1,1,1]=>8
[1,2,1,2]=>14
[1,2,2,1]=>28
[1,2,3]=>24
[1,3,1,1]=>24
[1,3,2]=>36
[1,4,1]=>32
[1,5]=>16
[2,1,1,1,1]=>10
[2,1,1,2]=>18
[2,1,2,1]=>36
[2,1,3]=>32
[2,2,1,1]=>54
[2,2,2]=>82
[2,3,1]=>96
[2,4]=>56
[3,1,1,1]=>40
[3,1,2]=>64
[3,2,1]=>128
[3,3]=>100
[4,1,1]=>80
[4,2]=>112
[5,1]=>80
[6]=>32
[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,2]=>2
[1,1,1,1,2,1]=>4
[1,1,1,1,3]=>4
[1,1,1,2,1,1]=>6
[1,1,1,2,2]=>10
[1,1,1,3,1]=>12
[1,1,1,4]=>8
[1,1,2,1,1,1]=>8
[1,1,2,1,2]=>14
[1,1,2,2,1]=>28
[1,1,2,3]=>24
[1,1,3,1,1]=>24
[1,1,3,2]=>36
[1,1,4,1]=>32
[1,1,5]=>16
[1,2,1,1,1,1]=>10
[1,2,1,1,2]=>18
[1,2,1,2,1]=>36
[1,2,1,3]=>32
[1,2,2,1,1]=>54
[1,2,2,2]=>82
[1,2,3,1]=>96
[1,2,4]=>56
[1,3,1,1,1]=>40
[1,3,1,2]=>64
[1,3,2,1]=>128
[1,3,3]=>100
[1,4,1,1]=>80
[1,4,2]=>112
[1,5,1]=>80
[1,6]=>32
[2,1,1,1,1,1]=>12
[2,1,1,1,2]=>22
[2,1,1,2,1]=>44
[2,1,1,3]=>40
[2,1,2,1,1]=>66
[2,1,2,2]=>102
[2,1,3,1]=>120
[2,1,4]=>72
[2,2,1,1,1]=>88
[2,2,1,2]=>142
[2,2,2,1]=>284
[2,2,3]=>224
[2,3,1,1]=>240
[2,3,2]=>336
[2,4,1]=>288
[2,5]=>128
[3,1,1,1,1]=>60
[3,1,1,2]=>100
[3,1,2,1]=>200
[3,1,3]=>164
[3,2,1,1]=>300
[3,2,2]=>428
[3,3,1]=>492
[3,4]=>264
[4,1,1,1]=>160
[4,1,2]=>240
[4,2,1]=>480
[4,3]=>352
[5,1,1]=>240
[5,2]=>320
[6,1]=>192
[7]=>64
[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,2]=>2
[1,1,1,1,1,2,1]=>4
[1,1,1,1,1,3]=>4
[1,1,1,1,2,1,1]=>6
[1,1,1,1,2,2]=>10
[1,1,1,1,3,1]=>12
[1,1,1,1,4]=>8
[1,1,1,2,1,1,1]=>8
[1,1,1,2,1,2]=>14
[1,1,1,2,2,1]=>28
[1,1,1,2,3]=>24
[1,1,1,3,1,1]=>24
[1,1,1,3,2]=>36
[1,1,1,4,1]=>32
[1,1,1,5]=>16
[1,1,2,1,1,1,1]=>10
[1,1,2,1,1,2]=>18
[1,1,2,1,2,1]=>36
[1,1,2,1,3]=>32
[1,1,2,2,1,1]=>54
[1,1,2,2,2]=>82
[1,1,2,3,1]=>96
[1,1,2,4]=>56
[1,1,3,1,1,1]=>40
[1,1,3,1,2]=>64
[1,1,3,2,1]=>128
[1,1,3,3]=>100
[1,1,4,1,1]=>80
[1,1,4,2]=>112
[1,1,5,1]=>80
[1,1,6]=>32
[1,2,1,1,1,1,1]=>12
[1,2,1,1,1,2]=>22
[1,2,1,1,2,1]=>44
[1,2,1,1,3]=>40
[1,2,1,2,1,1]=>66
[1,2,1,2,2]=>102
[1,2,1,3,1]=>120
[1,2,1,4]=>72
[1,2,2,1,1,1]=>88
[1,2,2,1,2]=>142
[1,2,2,2,1]=>284
[1,2,2,3]=>224
[1,2,3,1,1]=>240
[1,2,3,2]=>336
[1,2,4,1]=>288
[1,2,5]=>128
[1,3,1,1,1,1]=>60
[1,3,1,1,2]=>100
[1,3,1,2,1]=>200
[1,3,1,3]=>164
[1,3,2,1,1]=>300
[1,3,2,2]=>428
[1,3,3,1]=>492
[1,3,4]=>264
[1,4,1,1,1]=>160
[1,4,1,2]=>240
[1,4,2,1]=>480
[1,4,3]=>352
[1,5,1,1]=>240
[1,5,2]=>320
[1,6,1]=>192
[1,7]=>64
[2,1,1,1,1,1,1]=>14
[2,1,1,1,1,2]=>26
[2,1,1,1,2,1]=>52
[2,1,1,1,3]=>48
[2,1,1,2,1,1]=>78
[2,1,1,2,2]=>122
[2,1,1,3,1]=>144
[2,1,1,4]=>88
[2,1,2,1,1,1]=>104
[2,1,2,1,2]=>170
[2,1,2,2,1]=>340
[2,1,2,3]=>272
[2,1,3,1,1]=>288
[2,1,3,2]=>408
[2,1,4,1]=>352
[2,1,5]=>160
[2,2,1,1,1,1]=>130
[2,2,1,1,2]=>218
[2,2,1,2,1]=>436
[2,2,1,3]=>360
[2,2,2,1,1]=>654
[2,2,2,2]=>938
[2,2,3,1]=>1080
[2,2,4]=>584
[2,3,1,1,1]=>480
[2,3,1,2]=>720
[2,3,2,1]=>1440
[2,3,3]=>1056
[2,4,1,1]=>880
[2,4,2]=>1168
[2,5,1]=>800
[2,6]=>288
[3,1,1,1,1,1]=>84
[3,1,1,1,2]=>144
[3,1,1,2,1]=>288
[3,1,1,3]=>244
[3,1,2,1,1]=>432
[3,1,2,2]=>632
[3,1,3,1]=>732
[3,1,4]=>408
[3,2,1,1,1]=>576
[3,2,1,2]=>876
[3,2,2,1]=>1752
[3,2,3]=>1304
[3,3,1,1]=>1464
[3,3,2]=>1956
[3,4,1]=>1632
[3,5]=>672
[4,1,1,1,1]=>280
[4,1,1,2]=>440
[4,1,2,1]=>880
[4,1,3]=>680
[4,2,1,1]=>1320
[4,2,2]=>1800
[4,3,1]=>2040
[4,4]=>1032
[5,1,1,1]=>560
[5,1,2]=>800
[5,2,1]=>1600
[5,3]=>1120
[6,1,1]=>672
[6,2]=>864
[7,1]=>448
[8]=>128
[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,2]=>2
[1,1,1,1,1,1,2,1]=>4
[1,1,1,1,1,1,3]=>4
[1,1,1,1,1,2,1,1]=>6
[1,1,1,1,1,2,2]=>10
[1,1,1,1,1,3,1]=>12
[1,1,1,1,1,4]=>8
[1,1,1,1,2,1,1,1]=>8
[1,1,1,1,2,1,2]=>14
[1,1,1,1,2,2,1]=>28
[1,1,1,1,2,3]=>24
[1,1,1,1,3,1,1]=>24
[1,1,1,1,3,2]=>36
[1,1,1,1,4,1]=>32
[1,1,1,1,5]=>16
[1,1,1,2,1,1,1,1]=>10
[1,1,1,2,1,1,2]=>18
[1,1,1,2,1,2,1]=>36
[1,1,1,2,1,3]=>32
[1,1,1,2,2,1,1]=>54
[1,1,1,2,2,2]=>82
[1,1,1,2,3,1]=>96
[1,1,1,2,4]=>56
[1,1,1,3,1,1,1]=>40
[1,1,1,3,1,2]=>64
[1,1,1,3,2,1]=>128
[1,1,1,3,3]=>100
[1,1,1,4,1,1]=>80
[1,1,1,4,2]=>112
[1,1,1,5,1]=>80
[1,1,1,6]=>32
[1,1,2,1,1,1,1,1]=>12
[1,1,2,1,1,1,2]=>22
[1,1,2,1,1,2,1]=>44
[1,1,2,1,1,3]=>40
[1,1,2,1,2,1,1]=>66
[1,1,2,1,2,2]=>102
[1,1,2,1,3,1]=>120
[1,1,2,1,4]=>72
[1,1,2,2,1,1,1]=>88
[1,1,2,2,1,2]=>142
[1,1,2,2,2,1]=>284
[1,1,2,2,3]=>224
[1,1,2,3,1,1]=>240
[1,1,2,3,2]=>336
[1,1,2,4,1]=>288
[1,1,2,5]=>128
[1,1,3,1,1,1,1]=>60
[1,1,3,1,1,2]=>100
[1,1,3,1,2,1]=>200
[1,1,3,1,3]=>164
[1,1,3,2,1,1]=>300
[1,1,3,2,2]=>428
[1,1,3,3,1]=>492
[1,1,3,4]=>264
[1,1,4,1,1,1]=>160
[1,1,4,1,2]=>240
[1,1,4,2,1]=>480
[1,1,4,3]=>352
[1,1,5,1,1]=>240
[1,1,5,2]=>320
[1,1,6,1]=>192
[1,1,7]=>64
[1,2,1,1,1,1,1,1]=>14
[1,2,1,1,1,1,2]=>26
[1,2,1,1,1,2,1]=>52
[1,2,1,1,1,3]=>48
[1,2,1,1,2,1,1]=>78
[1,2,1,1,2,2]=>122
[1,2,1,1,3,1]=>144
[1,2,1,1,4]=>88
[1,2,1,2,1,1,1]=>104
[1,2,1,2,1,2]=>170
[1,2,1,2,2,1]=>340
[1,2,1,2,3]=>272
[1,2,1,3,1,1]=>288
[1,2,1,3,2]=>408
[1,2,1,4,1]=>352
[1,2,1,5]=>160
[1,2,2,1,1,1,1]=>130
[1,2,2,1,1,2]=>218
[1,2,2,1,2,1]=>436
[1,2,2,1,3]=>360
[1,2,2,2,1,1]=>654
[1,2,2,2,2]=>938
[1,2,2,3,1]=>1080
[1,2,2,4]=>584
[1,2,3,1,1,1]=>480
[1,2,3,1,2]=>720
[1,2,3,2,1]=>1440
[1,2,3,3]=>1056
[1,2,4,1,1]=>880
[1,2,4,2]=>1168
[1,2,5,1]=>800
[1,2,6]=>288
[1,3,1,1,1,1,1]=>84
[1,3,1,1,1,2]=>144
[1,3,1,1,2,1]=>288
[1,3,1,1,3]=>244
[1,3,1,2,1,1]=>432
[1,3,1,2,2]=>632
[1,3,1,3,1]=>732
[1,3,1,4]=>408
[1,3,2,1,1,1]=>576
[1,3,2,1,2]=>876
[1,3,2,2,1]=>1752
[1,3,2,3]=>1304
[1,3,3,1,1]=>1464
[1,3,3,2]=>1956
[1,3,4,1]=>1632
[1,3,5]=>672
[1,4,1,1,1,1]=>280
[1,4,1,1,2]=>440
[1,4,1,2,1]=>880
[1,4,1,3]=>680
[1,4,2,1,1]=>1320
[1,4,2,2]=>1800
[1,4,3,1]=>2040
[1,4,4]=>1032
[1,5,1,1,1]=>560
[1,5,1,2]=>800
[1,5,2,1]=>1600
[1,5,3]=>1120
[1,6,1,1]=>672
[1,6,2]=>864
[1,7,1]=>448
[1,8]=>128
[2,1,1,1,1,1,1,1]=>16
[2,1,1,1,1,1,2]=>30
[2,1,1,1,1,2,1]=>60
[2,1,1,1,1,3]=>56
[2,1,1,1,2,1,1]=>90
[2,1,1,1,2,2]=>142
[2,1,1,1,3,1]=>168
[2,1,1,1,4]=>104
[2,1,1,2,1,1,1]=>120
[2,1,1,2,1,2]=>198
[2,1,1,2,2,1]=>396
[2,1,1,2,3]=>320
[2,1,1,3,1,1]=>336
[2,1,1,3,2]=>480
[2,1,1,4,1]=>416
[2,1,1,5]=>192
[2,1,2,1,1,1,1]=>150
[2,1,2,1,1,2]=>254
[2,1,2,1,2,1]=>508
[2,1,2,1,3]=>424
[2,1,2,2,1,1]=>762
[2,1,2,2,2]=>1102
[2,1,2,3,1]=>1272
[2,1,2,4]=>696
[2,1,3,1,1,1]=>560
[2,1,3,1,2]=>848
[2,1,3,2,1]=>1696
[2,1,3,3]=>1256
[2,1,4,1,1]=>1040
[2,1,4,2]=>1392
[2,1,5,1]=>960
[2,1,6]=>352
[2,2,1,1,1,1,1]=>180
[2,2,1,1,1,2]=>310
[2,2,1,1,2,1]=>620
[2,2,1,1,3]=>528
[2,2,1,2,1,1]=>930
[2,2,1,2,2]=>1366
[2,2,1,3,1]=>1584
[2,2,1,4]=>888
[2,2,2,1,1,1]=>1240
[2,2,2,1,2]=>1894
[2,2,2,2,1]=>3788
[2,2,2,3]=>2832
[2,2,3,1,1]=>3168
[2,2,3,2]=>4248
[2,2,4,1]=>3552
[2,2,5]=>1472
[2,3,1,1,1,1]=>840
[2,3,1,1,2]=>1320
[2,3,1,2,1]=>2640
[2,3,1,3]=>2040
[2,3,2,1,1]=>3960
[2,3,2,2]=>5400
[2,3,3,1]=>6120
[2,3,4]=>3096
[2,4,1,1,1]=>2080
[2,4,1,2]=>2960
[2,4,2,1]=>5920
[2,4,3]=>4128
[2,5,1,1]=>2880
[2,5,2]=>3680
[2,6,1]=>2112
[2,7]=>640
[3,1,1,1,1,1,1]=>112
[3,1,1,1,1,2]=>196
[3,1,1,1,2,1]=>392
[3,1,1,1,3]=>340
[3,1,1,2,1,1]=>588
[3,1,1,2,2]=>876
[3,1,1,3,1]=>1020
[3,1,1,4]=>584
[3,1,2,1,1,1]=>784
[3,1,2,1,2]=>1216
[3,1,2,2,1]=>2432
[3,1,2,3]=>1848
[3,1,3,1,1]=>2040
[3,1,3,2]=>2772
[3,1,4,1]=>2336
[3,1,5]=>992
[3,2,1,1,1,1]=>980
[3,2,1,1,2]=>1556
[3,2,1,2,1]=>3112
[3,2,1,3]=>2432
[3,2,2,1,1]=>4668
[3,2,2,2]=>6420
[3,2,3,1]=>7296
[3,2,4]=>3736
[3,3,1,1,1]=>3400
[3,3,1,2]=>4864
[3,3,2,1]=>9728
[3,3,3]=>6820
[3,4,1,1]=>5840
[3,4,2]=>7472
[3,5,1]=>4960
[3,6]=>1664
[4,1,1,1,1,1]=>448
[4,1,1,1,2]=>728
[4,1,1,2,1]=>1456
[4,1,1,3]=>1168
[4,1,2,1,1]=>2184
[4,1,2,2]=>3064
[4,1,3,1]=>3504
[4,1,4]=>1848
[4,2,1,1,1]=>2912
[4,2,1,2]=>4232
[4,2,2,1]=>8464
[4,2,3]=>6032
[4,3,1,1]=>7008
[4,3,2]=>9048
[4,4,1]=>7392
[4,5]=>2880
[5,1,1,1,1]=>1120
[5,1,1,2]=>1680
[5,1,2,1]=>3360
[5,1,3]=>2480
[5,2,1,1]=>5040
[5,2,2]=>6640
[5,3,1]=>7440
[5,4]=>3600
[6,1,1,1]=>1792
[6,1,2]=>2464
[6,2,1]=>4928
[6,3]=>3328
[7,1,1]=>1792
[7,2]=>2240
[8,1]=>1024
[9]=>256
                    

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$F_{2} = q + q^{2}$

$F_{3} = q + q^{2} + 2\ q^{4}$

$F_{4} = q + q^{2} + 2\ q^{4} + q^{6} + q^{8} + q^{10} + q^{12}$

$F_{5} = q + q^{2} + 2\ q^{4} + q^{6} + 2\ q^{8} + q^{10} + q^{12} + q^{14} + q^{16} + 2\ q^{24} + q^{28} + q^{32} + q^{36}$

$F_{6} = q + q^{2} + 2\ q^{4} + q^{6} + 2\ q^{8} + 2\ q^{10} + q^{12} + q^{14} + q^{16} + q^{18} + 2\ q^{24} + q^{28} + 3\ q^{32} + 2\ q^{36} + q^{40} + q^{54} + q^{56} + q^{64} + 2\ q^{80} + q^{82} + q^{96} + q^{100} + q^{112} + q^{128}$

$F_{7} = q + q^{2} + 2\ q^{4} + q^{6} + 2\ q^{8} + 2\ q^{10} + 2\ q^{12} + q^{14} + q^{16} + q^{18} + q^{22} + 2\ q^{24} + q^{28} + 3\ q^{32} + 2\ q^{36} + 2\ q^{40} + q^{44} + q^{54} + q^{56} + q^{60} + 2\ q^{64} + q^{66} + q^{72} + 2\ q^{80} + q^{82} + q^{88} + q^{96} + 2\ q^{100} + q^{102} + q^{112} + q^{120} + 2\ q^{128} + q^{142} + q^{160} + q^{164} + q^{192} + q^{200} + q^{224} + 3\ q^{240} + q^{264} + q^{284} + q^{288} + q^{300} + q^{320} + q^{336} + q^{352} + q^{428} + q^{480} + q^{492}$

$F_{8} = q + q^{2} + 2\ q^{4} + q^{6} + 2\ q^{8} + 2\ q^{10} + 2\ q^{12} + 2\ q^{14} + q^{16} + q^{18} + q^{22} + 2\ q^{24} + q^{26} + q^{28} + 3\ q^{32} + 2\ q^{36} + 2\ q^{40} + q^{44} + q^{48} + q^{52} + q^{54} + q^{56} + q^{60} + 2\ q^{64} + q^{66} + q^{72} + q^{78} + 2\ q^{80} + q^{82} + q^{84} + 2\ q^{88} + q^{96} + 2\ q^{100} + q^{102} + q^{104} + q^{112} + q^{120} + q^{122} + 3\ q^{128} + q^{130} + q^{142} + 2\ q^{144} + 2\ q^{160} + q^{164} + q^{170} + q^{192} + q^{200} + q^{218} + q^{224} + 3\ q^{240} + q^{244} + q^{264} + q^{272} + q^{280} + q^{284} + 4\ q^{288} + q^{300} + q^{320} + q^{336} + q^{340} + 2\ q^{352} + q^{360} + 2\ q^{408} + q^{428} + q^{432} + q^{436} + q^{440} + q^{448} + 2\ q^{480} + q^{492} + q^{560} + q^{576} + q^{584} + q^{632} + q^{654} + 2\ q^{672} + q^{680} + q^{720} + q^{732} + 2\ q^{800} + q^{864} + q^{876} + 2\ q^{880} + q^{938} + q^{1032} + q^{1056} + q^{1080} + q^{1120} + q^{1168} + q^{1304} + q^{1320} + q^{1440} + q^{1464} + q^{1600} + q^{1632} + q^{1752} + q^{1800} + q^{1956} + q^{2040}$

$F_{9} = q + q^{2} + 2\ q^{4} + q^{6} + 2\ q^{8} + 2\ q^{10} + 2\ q^{12} + 2\ q^{14} + 2\ q^{16} + q^{18} + q^{22} + 2\ q^{24} + q^{26} + q^{28} + q^{30} + 3\ q^{32} + 2\ q^{36} + 2\ q^{40} + q^{44} + q^{48} + q^{52} + q^{54} + 2\ q^{56} + 2\ q^{60} + 2\ q^{64} + q^{66} + q^{72} + q^{78} + 2\ q^{80} + q^{82} + q^{84} + 2\ q^{88} + q^{90} + q^{96} + 2\ q^{100} + q^{102} + 2\ q^{104} + 2\ q^{112} + 2\ q^{120} + q^{122} + 3\ q^{128} + q^{130} + 2\ q^{142} + 2\ q^{144} + q^{150} + 2\ q^{160} + q^{164} + q^{168} + q^{170} + q^{180} + 2\ q^{192} + q^{196} + q^{198} + q^{200} + q^{218} + q^{224} + 3\ q^{240} + q^{244} + q^{254} + q^{256} + q^{264} + q^{272} + q^{280} + q^{284} + 4\ q^{288} + q^{300} + q^{310} + 2\ q^{320} + 2\ q^{336} + 2\ q^{340} + 3\ q^{352} + q^{360} + q^{392} + q^{396} + 2\ q^{408} + q^{416} + q^{424} + q^{428} + q^{432} + q^{436} + q^{440} + 2\ q^{448} + 3\ q^{480} + q^{492} + q^{508} + q^{528} + 2\ q^{560} + q^{576} + 2\ q^{584} + q^{588} + q^{620} + q^{632} + q^{640} + q^{654} + 2\ q^{672} + q^{680} + q^{696} + q^{720} + q^{728} + q^{732} + q^{762} + q^{784} + 2\ q^{800} + q^{840} + q^{848} + q^{864} + 2\ q^{876} + 2\ q^{880} + q^{888} + q^{930} + q^{938} + q^{960} + q^{980} + q^{992} + q^{1020} + q^{1024} + q^{1032} + q^{1040} + q^{1056} + q^{1080} + q^{1102} + 2\ q^{1120} + 2\ q^{1168} + q^{1216} + q^{1240} + q^{1256} + q^{1272} + q^{1304} + 2\ q^{1320} + q^{1366} + q^{1392} + q^{1440} + q^{1456} + q^{1464} + q^{1472} + q^{1556} + q^{1584} + q^{1600} + q^{1632} + q^{1664} + q^{1680} + q^{1696} + q^{1752} + 2\ q^{1792} + q^{1800} + 2\ q^{1848} + q^{1894} + q^{1956} + 3\ q^{2040} + q^{2080} + q^{2112} + q^{2184} + q^{2240} + q^{2336} + 2\ q^{2432} + q^{2464} + q^{2480} + q^{2640} + q^{2772} + q^{2832} + 2\ q^{2880} + q^{2912} + q^{2960} + q^{3064} + q^{3096} + q^{3112} + q^{3168} + q^{3328} + q^{3360} + q^{3400} + q^{3504} + q^{3552} + q^{3600} + q^{3680} + q^{3736} + q^{3788} + q^{3960} + q^{4128} + q^{4232} + q^{4248} + q^{4668} + q^{4864} + q^{4928} + q^{4960} + q^{5040} + q^{5400} + q^{5840} + q^{5920} + q^{6032} + q^{6120} + q^{6420} + q^{6640} + q^{6820} + q^{7008} + q^{7296} + q^{7392} + q^{7440} + q^{7472} + q^{8464} + q^{9048} + q^{9728}$

Description

The sum of the entries in the column specified by the composition of the change of basis matrix from dual immaculate quasisymmetric functions to monomial quasisymmetric functions.
For example, $dI_{121} = 2M_{1111} + M_{112} + M_{121}$, so the statistic on the composition $121$ is 4.

Code

def statistic(mu):
    M = QuasiSymmetricFunctions(ZZ).M()
    dI = QuasiSymmetricFunctions(ZZ).dI()
    return sum(coeff for _, coeff in M(dI(mu)))

Created

May 20, 2017 at 22:06 by Martin Rubey

Updated

May 20, 2017 at 22:06 by Martin Rubey