- FindStat

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Identifier

St000634: Posets ⟶ ℤ

Values

=>
                            Cc0014;cc-rep
                            
                            
                            

                        ([],2)=>4
([(0,1)],2)=>3
([],3)=>27
([(1,2)],3)=>12
([(0,1),(0,2)],3)=>11
([(0,2),(2,1)],3)=>10
([(0,2),(1,2)],3)=>11
([],4)=>256
([(2,3)],4)=>80
([(1,2),(1,3)],4)=>48
([(0,1),(0,2),(0,3)],4)=>67
([(0,2),(0,3),(3,1)],4)=>40
([(0,1),(0,2),(1,3),(2,3)],4)=>36
([(1,2),(2,3)],4)=>44
([(0,3),(3,1),(3,2)],4)=>40
([(1,3),(2,3)],4)=>48
([(0,3),(1,3),(3,2)],4)=>40
([(0,3),(1,3),(2,3)],4)=>67
([(0,3),(1,2)],4)=>36
([(0,3),(1,2),(1,3)],4)=>31
([(0,2),(0,3),(1,2),(1,3)],4)=>36
([(0,3),(2,1),(3,2)],4)=>35
([(0,3),(1,2),(2,3)],4)=>40
([],5)=>3125
([(3,4)],5)=>750
([(2,3),(2,4)],5)=>325
([(1,2),(1,3),(1,4)],5)=>340
([(0,1),(0,2),(0,3),(0,4)],5)=>629
([(0,2),(0,3),(0,4),(4,1)],5)=>265
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)=>167
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>178
([(1,3),(1,4),(4,2)],5)=>205
([(0,3),(0,4),(4,1),(4,2)],5)=>221
([(1,2),(1,3),(2,4),(3,4)],5)=>185
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>133
([(0,3),(0,4),(3,2),(4,1)],5)=>141
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>135
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)=>133
([(2,3),(3,4)],5)=>300
([(1,4),(4,2),(4,3)],5)=>205
([(0,4),(4,1),(4,2),(4,3)],5)=>262
([(2,4),(3,4)],5)=>325
([(1,4),(2,4),(4,3)],5)=>205
([(0,4),(1,4),(4,2),(4,3)],5)=>145
([(1,4),(2,4),(3,4)],5)=>340
([(0,4),(1,4),(2,4),(4,3)],5)=>262
([(0,4),(1,4),(2,4),(3,4)],5)=>629
([(0,4),(1,4),(2,3)],5)=>128
([(0,4),(1,3),(2,3),(2,4)],5)=>99
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>145
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>197
([(0,4),(1,4),(2,3),(4,2)],5)=>147
([(0,4),(1,3),(2,3),(3,4)],5)=>221
([(0,4),(1,4),(2,3),(2,4)],5)=>151
([(0,4),(1,4),(2,3),(3,4)],5)=>265
([(1,4),(2,3)],5)=>245
([(1,4),(2,3),(2,4)],5)=>160
([(0,4),(1,2),(1,4),(2,3)],5)=>105
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)=>135
([(1,3),(1,4),(2,3),(2,4)],5)=>185
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)=>130
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)=>133
([(0,4),(1,2),(1,4),(4,3)],5)=>129
([(0,4),(1,2),(1,3)],5)=>128
([(0,4),(1,2),(1,3),(1,4)],5)=>151
([(0,2),(0,4),(3,1),(4,3)],5)=>155
([(0,4),(1,2),(1,3),(3,4)],5)=>128
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>136
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>167
([(0,3),(0,4),(1,2),(1,4)],5)=>99
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>145
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>197
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)=>109
([(0,3),(1,2),(1,4),(3,4)],5)=>105
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)=>130
([(1,4),(3,2),(4,3)],5)=>180
([(0,3),(3,4),(4,1),(4,2)],5)=>147
([(1,4),(2,3),(3,4)],5)=>205
([(0,4),(1,2),(2,4),(4,3)],5)=>154
([(0,3),(1,4),(4,2)],5)=>126
([(0,4),(3,2),(4,1),(4,3)],5)=>154
([(0,4),(1,2),(2,3),(2,4)],5)=>129
([(0,4),(2,3),(3,1),(4,2)],5)=>126
([(0,3),(1,2),(2,4),(3,4)],5)=>141
([(0,4),(1,2),(2,3),(3,4)],5)=>155
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>133
([],6)=>46656
([(4,5)],6)=>9072
([(3,4),(3,5)],6)=>3024
([(2,3),(2,4),(2,5)],6)=>2484
([(1,2),(1,3),(1,4),(1,5)],6)=>3780
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)=>7781
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)=>2620
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)=>1231
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)=>1004
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)=>1430
([(1,3),(1,4),(1,5),(5,2)],6)=>1596
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)=>1867
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)=>1008
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>1074
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)=>693
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)=>579
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)=>490
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>533
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>586
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)=>611
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)=>650
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)=>680
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)=>1053
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)=>868
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)=>783
([(2,3),(2,4),(4,5)],6)=>1512
([(1,4),(1,5),(5,2),(5,3)],6)=>1332
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)=>1976
([(2,3),(2,4),(3,5),(4,5)],6)=>1368
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)=>804
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)=>517
([(1,4),(1,5),(4,3),(5,2)],6)=>852
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)=>816
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>804
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)=>509
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>477
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)=>533
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)=>801
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)=>901
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)=>652
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)=>745
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>824
([(3,4),(4,5)],6)=>2808
([(2,3),(3,4),(3,5)],6)=>1512
([(1,5),(5,2),(5,3),(5,4)],6)=>1578
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)=>2558
([(2,3),(3,5),(5,4)],6)=>1332
([(1,4),(4,5),(5,2),(5,3)],6)=>888
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)=>1005
([(3,5),(4,5)],6)=>3024
([(2,5),(3,5),(5,4)],6)=>1512
([(1,5),(2,5),(5,3),(5,4)],6)=>876
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)=>874
([(2,5),(3,5),(4,5)],6)=>2484
([(1,5),(2,5),(3,5),(5,4)],6)=>1578
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)=>874
([(1,5),(2,5),(3,5),(4,5)],6)=>3780
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)=>2558
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>7781
([(0,5),(1,5),(2,5),(3,4)],6)=>760
([(0,5),(1,5),(2,5),(3,4),(5,3)],6)=>1005
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)=>1976
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)=>1291
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>2620
([(1,5),(2,5),(3,4)],6)=>918
([(1,5),(2,4),(3,4),(3,5)],6)=>600
([(0,5),(1,4),(2,4),(2,5),(5,3)],6)=>406
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)=>652
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>876
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)=>472
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)=>745
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>1188
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)=>704
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>824
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)=>650
([(1,5),(2,5),(3,4),(5,3)],6)=>888
([(1,5),(2,4),(3,4),(4,5)],6)=>1332
([(0,5),(1,4),(2,4),(4,5),(5,3)],6)=>918
([(0,5),(1,5),(2,3),(5,4)],6)=>552
([(0,5),(1,5),(4,2),(5,3),(5,4)],6)=>555
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)=>629
([(1,5),(2,5),(3,4),(3,5)],6)=>912
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)=>763
([(0,5),(1,5),(2,3),(2,5),(3,4)],6)=>406
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)=>901
([(0,5),(1,5),(2,3),(2,4)],6)=>400
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)=>573
([(0,4),(1,4),(2,3),(2,5),(4,5)],6)=>561
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>650
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)=>560
([(0,5),(1,2),(1,4),(3,5),(4,3)],6)=>603
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)=>704
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>493
([(0,5),(1,5),(2,3),(2,4),(4,5)],6)=>709
([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6)=>717
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>650
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>1231
([(1,5),(2,5),(3,4),(4,5)],6)=>1596
([(0,5),(1,5),(2,3),(3,5),(5,4)],6)=>1122
([(0,5),(1,5),(2,3),(3,4)],6)=>425
([(0,5),(1,5),(3,2),(4,3),(5,4)],6)=>546
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)=>801
([(0,5),(1,4),(3,5),(4,2),(4,3)],6)=>581
([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)=>700
([(0,5),(1,5),(2,3),(3,4),(3,5)],6)=>640
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>1045
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)=>680
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)=>693
([(0,5),(1,5),(2,4),(3,4)],6)=>484
([(0,5),(1,5),(2,4),(3,4),(3,5)],6)=>509
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>970
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>692
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>1167
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>1782
([(0,5),(1,4),(2,4),(3,5),(4,3)],6)=>832
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)=>517
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>1867
([(2,5),(3,4)],6)=>2304
([(2,5),(3,4),(3,5)],6)=>1188
([(1,5),(2,3),(2,5),(3,4)],6)=>636
([(0,5),(1,4),(1,5),(4,2),(4,3)],6)=>561
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)=>401
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)=>427
([(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>816
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)=>556
([(0,5),(1,4),(1,5),(4,2),(5,3)],6)=>378
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)=>426
([(2,4),(2,5),(3,4),(3,5)],6)=>1368
([(1,4),(1,5),(2,4),(2,5),(5,3)],6)=>786
([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)=>650
([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>804
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)=>418
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)=>427
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)=>446
([(0,4),(0,5),(1,4),(1,5),(2,3)],6)=>473
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)=>538
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)=>529
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)=>496
([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6)=>562
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>783
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6)=>396
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6)=>524
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>626
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)=>552
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6)=>471
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)=>737
([(1,5),(2,3),(2,5),(5,4)],6)=>780
([(0,5),(1,2),(1,5),(5,3),(5,4)],6)=>629
([(1,5),(2,3),(2,4)],6)=>918
([(1,5),(2,3),(2,4),(2,5)],6)=>912
([(0,5),(1,3),(1,4),(1,5),(4,2)],6)=>612
([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6)=>510
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5)],6)=>435
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>611
([(0,5),(1,2),(1,3),(1,5),(5,4)],6)=>640
([(0,5),(1,2),(1,3),(1,4)],6)=>760
([(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>1291
([(0,2),(0,3),(0,5),(4,1),(5,4)],6)=>1045
([(0,5),(1,2),(1,3),(1,4),(4,5)],6)=>709
([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6)=>717
([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6)=>662
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)=>774
([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>1004
([(0,4),(1,2),(1,3),(1,5),(4,5)],6)=>406
([(0,3),(1,2),(1,4),(1,5),(3,4),(3,5)],6)=>472
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>704
([(1,3),(1,5),(4,2),(5,4)],6)=>936
([(0,3),(0,4),(4,5),(5,1),(5,2)],6)=>832
([(0,4),(0,5),(3,2),(4,3),(5,1)],6)=>521
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)=>515
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>500
([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6)=>475
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)=>481
([(1,5),(2,3),(2,4),(4,5)],6)=>774
([(0,5),(1,2),(1,3),(3,5),(5,4)],6)=>581
([(1,3),(1,4),(2,5),(3,5),(4,2)],6)=>822
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>519
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>1008
([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)=>700
([(0,5),(1,3),(1,4),(3,5),(4,2)],6)=>418
([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6)=>433
([(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>523
([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6)=>605
([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6)=>605
([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6)=>510
([(0,4),(1,3),(1,5),(5,2)],6)=>517
([(0,3),(0,5),(4,2),(5,1),(5,4)],6)=>963
([(0,5),(1,3),(1,4),(4,2),(4,5)],6)=>619
([(0,4),(1,2),(1,3),(3,5),(4,5)],6)=>418
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>550
([(0,4),(1,2),(1,3),(2,5),(3,5)],6)=>504
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>579
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>496
([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6)=>704
([(1,4),(1,5),(2,3),(2,5)],6)=>600
([(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>876
([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)=>610
([(0,4),(0,5),(1,2),(1,4),(1,5),(4,3),(5,3)],6)=>523
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>1188
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)=>737
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)=>502
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>586
([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3)],6)=>471
([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6)=>421
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>533
([(0,4),(0,5),(1,3),(1,5),(5,2)],6)=>499
([(1,4),(1,5),(2,3),(2,4),(3,5)],6)=>660
([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6)=>362
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)=>470
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)=>481
([(0,3),(0,5),(1,4),(1,5),(4,2)],6)=>333
([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6)=>433
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5)],6)=>466
([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)=>373
([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5)],6)=>342
([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5),(4,5)],6)=>490
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)=>416
([(0,4),(0,5),(1,2),(1,3)],6)=>484
([(0,4),(0,5),(1,2),(1,3),(1,5)],6)=>509
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>970
([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6)=>513
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6)=>416
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6)=>692
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>1167
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>1782
([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6)=>552
([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6)=>418
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6)=>524
([(0,4),(0,5),(1,2),(1,3),(3,5)],6)=>388
([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6)=>562
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)=>496
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)=>528
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,5)],6)=>435
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>342
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6)=>421
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>502
([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6)=>302
([(1,4),(2,3),(2,5),(4,5)],6)=>636
([(0,4),(1,3),(1,5),(4,5),(5,2)],6)=>500
([(1,4),(1,5),(2,3),(3,4),(3,5)],6)=>786
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)=>490
([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>509
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)=>290
([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)=>515
([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6)=>362
([(0,5),(1,3),(1,4),(5,2)],6)=>425
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>641
([(0,5),(4,2),(4,3),(5,1),(5,4)],6)=>918
([(0,4),(1,3),(1,5),(4,2),(4,5)],6)=>406
([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5)],6)=>650
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)=>470
([(2,5),(3,4),(4,5)],6)=>1512
([(1,5),(2,3),(3,5),(5,4)],6)=>930
([(0,5),(1,2),(2,5),(5,3),(5,4)],6)=>555
([(1,3),(2,4),(4,5)],6)=>900
([(1,5),(4,3),(5,2),(5,4)],6)=>930
([(1,5),(2,3),(3,4),(3,5)],6)=>780
([(0,5),(1,4),(4,2),(4,5),(5,3)],6)=>523
([(0,4),(1,5),(5,2),(5,3)],6)=>552
([(0,5),(4,3),(5,1),(5,2),(5,4)],6)=>1122
([(0,5),(1,4),(4,2),(4,3),(4,5)],6)=>763
([(1,5),(3,4),(4,2),(5,3)],6)=>762
([(0,4),(3,5),(4,3),(5,1),(5,2)],6)=>546
([(1,4),(2,3),(3,5),(4,5)],6)=>852
([(0,4),(1,3),(3,5),(4,5),(5,2)],6)=>593
([(0,5),(1,4),(4,2),(5,3)],6)=>400
([(0,5),(3,4),(4,2),(5,1),(5,3)],6)=>606
([(0,3),(1,4),(3,5),(4,2),(4,5)],6)=>378
([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6)=>418
([(1,5),(2,3),(3,4),(4,5)],6)=>936
([(1,4),(2,5),(3,5),(4,2),(4,3)],6)=>804
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>494
([(0,5),(1,4),(2,5),(4,2),(5,3)],6)=>606
([(0,5),(1,4),(2,3)],6)=>729
([(0,5),(1,3),(2,4),(2,5)],6)=>390
([(0,5),(1,4),(2,3),(2,4),(2,5)],6)=>410
([(0,5),(1,4),(1,5),(3,2),(4,3)],6)=>440
([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>475
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>388
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)=>528
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>868
([(0,5),(1,3),(1,5),(4,2),(5,4)],6)=>571
([(0,5),(1,4),(2,3),(2,4),(4,5)],6)=>619
([(0,4),(1,4),(1,5),(2,3),(2,5)],6)=>275
([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>396
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>626
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6)=>234
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6)=>417
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>646
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>951
([(0,4),(1,3),(1,5),(2,3),(2,4),(4,5)],6)=>466
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>488
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)=>513
([(0,5),(1,4),(1,5),(2,3),(2,5)],6)=>410
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>418
([(0,4),(1,4),(1,5),(2,3),(3,5)],6)=>333
([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)=>610
([(0,4),(1,3),(1,5),(2,5),(4,2)],6)=>440
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)=>538
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)=>529
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)=>556
([(0,5),(1,4),(2,3),(2,5),(4,5)],6)=>612
([(0,5),(1,3),(4,2),(5,4)],6)=>520
([(0,5),(3,2),(4,1),(5,3),(5,4)],6)=>593
([(0,5),(1,4),(3,2),(4,3),(4,5)],6)=>500
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)=>533
([(0,4),(3,2),(4,5),(5,1),(5,3)],6)=>586
([(0,5),(1,3),(3,4),(4,2),(4,5)],6)=>571
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>462
([(0,5),(1,3),(2,4),(4,5)],6)=>517
([(0,5),(1,4),(2,3),(3,4),(3,5)],6)=>499
([(0,5),(1,3),(3,5),(4,2),(5,4)],6)=>586
([(0,5),(1,4),(2,3),(3,5),(5,4)],6)=>963
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)=>641
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>496
([(0,3),(1,4),(2,5),(3,5),(4,2)],6)=>521
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>519
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>1053
                    

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

$F_{3} = q^{10} + 2\ q^{11} + q^{12} + q^{27}$

$F_{4} = q^{31} + q^{35} + 3\ q^{36} + 4\ q^{40} + q^{44} + 2\ q^{48} + 2\ q^{67} + q^{80} + q^{256}$

$F_{5} = 2\ q^{99} + 2\ q^{105} + q^{109} + 2\ q^{126} + 3\ q^{128} + 2\ q^{129} + 2\ q^{130} + 4\ q^{133} + 2\ q^{135} + q^{136} + 2\ q^{141} + 3\ q^{145} + 2\ q^{147} + 2\ q^{151} + 2\ q^{154} + 2\ q^{155} + q^{160} + 2\ q^{167} + q^{178} + q^{180} + 2\ q^{185} + 2\ q^{197} + 4\ q^{205} + 2\ q^{221} + q^{245} + 2\ q^{262} + 2\ q^{265} + q^{300} + 2\ q^{325} + 2\ q^{340} + 2\ q^{629} + q^{750} + q^{3125}$

$F_{6} = q^{234} + q^{275} + q^{290} + q^{302} + 2\ q^{333} + 2\ q^{342} + 2\ q^{362} + q^{373} + 2\ q^{378} + 2\ q^{388} + q^{390} + 2\ q^{396} + 2\ q^{400} + q^{401} + 4\ q^{406} + 2\ q^{410} + 2\ q^{416} + q^{417} + 6\ q^{418} + 2\ q^{421} + 2\ q^{425} + q^{426} + 2\ q^{427} + 2\ q^{433} + 2\ q^{435} + 2\ q^{440} + q^{446} + q^{462} + 2\ q^{466} + 2\ q^{470} + 2\ q^{471} + 2\ q^{472} + q^{473} + 2\ q^{475} + q^{477} + 2\ q^{481} + 2\ q^{484} + q^{488} + 3\ q^{490} + q^{493} + q^{494} + 4\ q^{496} + 2\ q^{499} + 3\ q^{500} + 2\ q^{502} + q^{504} + 4\ q^{509} + 2\ q^{510} + 2\ q^{513} + 2\ q^{515} + 4\ q^{517} + 2\ q^{519} + q^{520} + 2\ q^{521} + 3\ q^{523} + 2\ q^{524} + 2\ q^{528} + 2\ q^{529} + 4\ q^{533} + 2\ q^{538} + 2\ q^{546} + q^{550} + 4\ q^{552} + 2\ q^{555} + 2\ q^{556} + q^{560} + 2\ q^{561} + 2\ q^{562} + 2\ q^{571} + q^{573} + 2\ q^{579} + 2\ q^{581} + 4\ q^{586} + 2\ q^{593} + 2\ q^{600} + q^{603} + 2\ q^{605} + 2\ q^{606} + 2\ q^{610} + 2\ q^{611} + 2\ q^{612} + 2\ q^{619} + 2\ q^{626} + 2\ q^{629} + 2\ q^{636} + 2\ q^{640} + 2\ q^{641} + q^{646} + 6\ q^{650} + 2\ q^{652} + q^{660} + q^{662} + 2\ q^{680} + 2\ q^{692} + 2\ q^{693} + 2\ q^{700} + 4\ q^{704} + 2\ q^{709} + 2\ q^{717} + q^{729} + 2\ q^{737} + 2\ q^{745} + 2\ q^{760} + q^{762} + 2\ q^{763} + 2\ q^{774} + 2\ q^{780} + 2\ q^{783} + 2\ q^{786} + 2\ q^{801} + 4\ q^{804} + 2\ q^{816} + q^{822} + 2\ q^{824} + 2\ q^{832} + 2\ q^{852} + 2\ q^{868} + 2\ q^{874} + 3\ q^{876} + 2\ q^{888} + q^{900} + 2\ q^{901} + 2\ q^{912} + 4\ q^{918} + 2\ q^{930} + 2\ q^{936} + q^{951} + 2\ q^{963} + 2\ q^{970} + 2\ q^{1004} + 2\ q^{1005} + 2\ q^{1008} + 2\ q^{1045} + 2\ q^{1053} + q^{1074} + 2\ q^{1122} + 2\ q^{1167} + 3\ q^{1188} + 2\ q^{1231} + 2\ q^{1291} + 3\ q^{1332} + 2\ q^{1368} + q^{1430} + 4\ q^{1512} + 2\ q^{1578} + 2\ q^{1596} + 2\ q^{1782} + 2\ q^{1867} + 2\ q^{1976} + q^{2304} + 2\ q^{2484} + 2\ q^{2558} + 2\ q^{2620} + q^{2808} + 2\ q^{3024} + 2\ q^{3780} + 2\ q^{7781} + q^{9072} + q^{46656}$

Description

The number of endomorphisms of a poset.

References

[1] Prince, R. Whether a total order set of size $n$ has the fewest endomorphisms among posets of size $n$ MathOverflow:252899

Code

def statistic(P):
    return len(poset_endomorphisms(P))

def poset_endomorphisms(P):
    P = P.relabel()
    r = P.cardinality()
    S = cartesian_product([range(r)]*r)
    return [pi for pi in S if P.is_poset_morphism(lambda i: pi[i], P)]

(* Mathematica code using depth first recursion *)

endoCount::usage := "If rel is a reflexive relation on 1,2,..,Max[rel], then \
endoCount[rel] is the number of self maps f for which {f[a],f[b]} is in the \
relation whenever {a,b} is in the relation.”

endoCount[rel_] := morphismCount[rel, rel]

morphismCount[rel1_List, rel2_List] :=
Module[{max1 = Max[rel1], max2 = Max[rel2], down, checkdown, num, ans},
 Do[down[i] = Select[rel1, Max[#] == i &], {i, max1}];
 checkdown[f_List] := AllTrue[down[Length[f]], MemberQ[rel2, f[[#1]]] &];
 num[{}] := Sum[num[{i}], {i, max2}];
 num[f_List] :=
  If[checkdown[f],
   If[Length[f] == max1, 1, Sum[num[Append[f, i]], {i, max2}]], 0];
 ans = num[{}]; Clear[checkdown, down]; ans]

(* example *)

endoCount[{{1, 1}, {1, 2}, {1, 10}, {2, 2}, {3, 2}, {3, 3}, {3,
  4}, {4, 4}, {5, 4}, {5, 5}, {5, 6}, {6, 6}, {7, 6}, {7, 7}, {7,
  8}, {8, 8}, {9, 8}, {9, 9}, {9, 10}, {10, 10}}]

(* gives 10030 *)

(* Sanity checks are to be added. For instance we must have 
  Union @@ rel == Range[Max[rel]]
*)

Created

Oct 24, 2016 at 12:49 by Martin Rubey

Updated

Nov 13, 2022 at 11:36 by Martin Rubey