Identifier
Identifier
Values
([],2) generating graphics... => 4
([(0,1)],2) generating graphics... => 3
([],3) generating graphics... => 27
([(1,2)],3) generating graphics... => 12
([(0,1),(0,2)],3) generating graphics... => 11
([(0,2),(2,1)],3) generating graphics... => 10
([(0,2),(1,2)],3) generating graphics... => 11
([],4) generating graphics... => 256
([(2,3)],4) generating graphics... => 80
([(1,2),(1,3)],4) generating graphics... => 48
([(0,1),(0,2),(0,3)],4) generating graphics... => 67
([(0,2),(0,3),(3,1)],4) generating graphics... => 40
([(0,1),(0,2),(1,3),(2,3)],4) generating graphics... => 36
([(1,2),(2,3)],4) generating graphics... => 44
([(0,3),(3,1),(3,2)],4) generating graphics... => 40
([(1,3),(2,3)],4) generating graphics... => 48
([(0,3),(1,3),(3,2)],4) generating graphics... => 40
([(0,3),(1,3),(2,3)],4) generating graphics... => 67
([(0,3),(1,2)],4) generating graphics... => 36
([(0,3),(1,2),(1,3)],4) generating graphics... => 31
([(0,2),(0,3),(1,2),(1,3)],4) generating graphics... => 36
([(0,3),(2,1),(3,2)],4) generating graphics... => 35
([(0,3),(1,2),(2,3)],4) generating graphics... => 40
([],5) generating graphics... => 3125
([(3,4)],5) generating graphics... => 750
([(2,3),(2,4)],5) generating graphics... => 325
([(1,2),(1,3),(1,4)],5) generating graphics... => 340
([(0,1),(0,2),(0,3),(0,4)],5) generating graphics... => 629
([(0,2),(0,3),(0,4),(4,1)],5) generating graphics... => 265
([(0,1),(0,2),(0,3),(2,4),(3,4)],5) generating graphics... => 167
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) generating graphics... => 178
([(1,3),(1,4),(4,2)],5) generating graphics... => 205
([(0,3),(0,4),(4,1),(4,2)],5) generating graphics... => 221
([(1,2),(1,3),(2,4),(3,4)],5) generating graphics... => 185
([(0,2),(0,3),(2,4),(3,4),(4,1)],5) generating graphics... => 133
([(0,3),(0,4),(3,2),(4,1)],5) generating graphics... => 141
([(0,2),(0,3),(2,4),(3,1),(3,4)],5) generating graphics... => 135
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 133
([(2,3),(3,4)],5) generating graphics... => 300
([(1,4),(4,2),(4,3)],5) generating graphics... => 205
([(0,4),(4,1),(4,2),(4,3)],5) generating graphics... => 262
([(2,4),(3,4)],5) generating graphics... => 325
([(1,4),(2,4),(4,3)],5) generating graphics... => 205
([(0,4),(1,4),(4,2),(4,3)],5) generating graphics... => 145
([(1,4),(2,4),(3,4)],5) generating graphics... => 340
([(0,4),(1,4),(2,4),(4,3)],5) generating graphics... => 262
([(0,4),(1,4),(2,4),(3,4)],5) generating graphics... => 629
([(0,4),(1,4),(2,3)],5) generating graphics... => 128
([(0,4),(1,3),(2,3),(2,4)],5) generating graphics... => 99
([(0,4),(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 145
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 197
([(0,4),(1,4),(2,3),(4,2)],5) generating graphics... => 147
([(0,4),(1,3),(2,3),(3,4)],5) generating graphics... => 221
([(0,4),(1,4),(2,3),(2,4)],5) generating graphics... => 151
([(0,4),(1,4),(2,3),(3,4)],5) generating graphics... => 265
([(1,4),(2,3)],5) generating graphics... => 245
([(1,4),(2,3),(2,4)],5) generating graphics... => 160
([(0,4),(1,2),(1,4),(2,3)],5) generating graphics... => 105
([(0,3),(1,2),(1,3),(2,4),(3,4)],5) generating graphics... => 135
([(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 185
([(0,3),(0,4),(1,3),(1,4),(4,2)],5) generating graphics... => 130
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) generating graphics... => 133
([(0,4),(1,2),(1,4),(4,3)],5) generating graphics... => 129
([(0,4),(1,2),(1,3)],5) generating graphics... => 128
([(0,4),(1,2),(1,3),(1,4)],5) generating graphics... => 151
([(0,2),(0,4),(3,1),(4,3)],5) generating graphics... => 155
([(0,4),(1,2),(1,3),(3,4)],5) generating graphics... => 128
([(0,2),(0,3),(1,4),(2,4),(3,1)],5) generating graphics... => 136
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) generating graphics... => 167
([(0,3),(0,4),(1,2),(1,4)],5) generating graphics... => 99
([(0,3),(0,4),(1,2),(1,3),(1,4)],5) generating graphics... => 145
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) generating graphics... => 197
([(0,3),(0,4),(1,2),(1,3),(2,4)],5) generating graphics... => 109
([(0,3),(1,2),(1,4),(3,4)],5) generating graphics... => 105
([(0,3),(0,4),(1,2),(2,3),(2,4)],5) generating graphics... => 130
([(1,4),(3,2),(4,3)],5) generating graphics... => 180
([(0,3),(3,4),(4,1),(4,2)],5) generating graphics... => 147
([(1,4),(2,3),(3,4)],5) generating graphics... => 205
([(0,4),(1,2),(2,4),(4,3)],5) generating graphics... => 154
([(0,3),(1,4),(4,2)],5) generating graphics... => 126
([(0,4),(3,2),(4,1),(4,3)],5) generating graphics... => 154
([(0,4),(1,2),(2,3),(2,4)],5) generating graphics... => 129
([(0,4),(2,3),(3,1),(4,2)],5) generating graphics... => 126
([(0,3),(1,2),(2,4),(3,4)],5) generating graphics... => 141
([(0,4),(1,2),(2,3),(3,4)],5) generating graphics... => 155
([(0,3),(1,4),(2,4),(3,1),(3,2)],5) generating graphics... => 133
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6) generating graphics... => 234
([(0,4),(1,4),(1,5),(2,3),(2,5)],6) generating graphics... => 275
([(0,3),(1,4),(1,5),(3,5),(4,2)],6) generating graphics... => 290
([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6) generating graphics... => 302
([(0,3),(0,5),(1,4),(1,5),(4,2)],6) generating graphics... => 333
([(0,4),(1,4),(1,5),(2,3),(3,5)],6) generating graphics... => 333
([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5)],6) generating graphics... => 342
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) generating graphics... => 342
([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6) generating graphics... => 362
([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6) generating graphics... => 362
([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) generating graphics... => 373
([(0,5),(1,4),(1,5),(4,2),(5,3)],6) generating graphics... => 378
([(0,3),(1,4),(3,5),(4,2),(4,5)],6) generating graphics... => 378
([(0,4),(0,5),(1,2),(1,3),(3,5)],6) generating graphics... => 388
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) generating graphics... => 388
([(0,5),(1,3),(2,4),(2,5)],6) generating graphics... => 390
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6) generating graphics... => 396
([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) generating graphics... => 396
([(0,5),(1,4),(4,2),(5,3)],6) generating graphics... => 400
([(0,5),(1,5),(2,3),(2,4)],6) generating graphics... => 400
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) generating graphics... => 401
([(0,4),(1,3),(1,5),(4,2),(4,5)],6) generating graphics... => 406
([(0,4),(1,2),(1,3),(1,5),(4,5)],6) generating graphics... => 406
([(0,5),(1,4),(2,4),(2,5),(5,3)],6) generating graphics... => 406
([(0,5),(1,5),(2,3),(2,5),(3,4)],6) generating graphics... => 406
([(0,5),(1,4),(2,3),(2,4),(2,5)],6) generating graphics... => 410
([(0,5),(1,4),(1,5),(2,3),(2,5)],6) generating graphics... => 410
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6) generating graphics... => 416
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6) generating graphics... => 416
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6) generating graphics... => 417
([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6) generating graphics... => 418
([(0,5),(1,3),(1,4),(3,5),(4,2)],6) generating graphics... => 418
([(0,4),(1,2),(1,3),(3,5),(4,5)],6) generating graphics... => 418
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) generating graphics... => 418
([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 418
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4)],6) generating graphics... => 418
([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6) generating graphics... => 421
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6) generating graphics... => 421
([(0,5),(1,3),(1,4),(5,2)],6) generating graphics... => 425
([(0,5),(1,5),(2,3),(3,4)],6) generating graphics... => 425
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) generating graphics... => 426
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) generating graphics... => 427
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) generating graphics... => 427
([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6) generating graphics... => 433
([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6) generating graphics... => 433
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,5)],6) generating graphics... => 435
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5)],6) generating graphics... => 435
([(0,5),(1,4),(1,5),(3,2),(4,3)],6) generating graphics... => 440
([(0,4),(1,3),(1,5),(2,5),(4,2)],6) generating graphics... => 440
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) generating graphics... => 446
([(0,5),(2,4),(3,2),(4,1),(5,3)],6) generating graphics... => 462
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5)],6) generating graphics... => 466
([(0,4),(1,3),(1,5),(2,3),(2,4),(4,5)],6) generating graphics... => 466
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) generating graphics... => 470
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) generating graphics... => 470
([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3)],6) generating graphics... => 471
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6) generating graphics... => 471
([(0,3),(1,2),(1,4),(1,5),(3,4),(3,5)],6) generating graphics... => 472
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6) generating graphics... => 472
([(0,4),(0,5),(1,4),(1,5),(2,3)],6) generating graphics... => 473
([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) generating graphics... => 475
([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6) generating graphics... => 475
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) generating graphics... => 477
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) generating graphics... => 481
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) generating graphics... => 481
([(0,4),(0,5),(1,2),(1,3)],6) generating graphics... => 484
([(0,5),(1,5),(2,4),(3,4)],6) generating graphics... => 484
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) generating graphics... => 488
([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5),(4,5)],6) generating graphics... => 490
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) generating graphics... => 490
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6) generating graphics... => 490
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) generating graphics... => 493
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) generating graphics... => 494
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) generating graphics... => 496
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) generating graphics... => 496
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) generating graphics... => 496
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) generating graphics... => 496
([(0,4),(0,5),(1,3),(1,5),(5,2)],6) generating graphics... => 499
([(0,5),(1,4),(2,3),(3,4),(3,5)],6) generating graphics... => 499
([(0,4),(1,3),(1,5),(4,5),(5,2)],6) generating graphics... => 500
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) generating graphics... => 500
([(0,5),(1,4),(3,2),(4,3),(4,5)],6) generating graphics... => 500
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 502
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6) generating graphics... => 502
([(0,4),(1,2),(1,3),(2,5),(3,5)],6) generating graphics... => 504
([(0,4),(0,5),(1,2),(1,3),(1,5)],6) generating graphics... => 509
([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) generating graphics... => 509
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) generating graphics... => 509
([(0,5),(1,5),(2,4),(3,4),(3,5)],6) generating graphics... => 509
([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6) generating graphics... => 510
([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6) generating graphics... => 510
([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) generating graphics... => 513
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) generating graphics... => 513
([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) generating graphics... => 515
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) generating graphics... => 515
([(0,4),(1,3),(1,5),(5,2)],6) generating graphics... => 517
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) generating graphics... => 517
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) generating graphics... => 517
([(0,5),(1,3),(2,4),(4,5)],6) generating graphics... => 517
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) generating graphics... => 519
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) generating graphics... => 519
([(0,5),(1,3),(4,2),(5,4)],6) generating graphics... => 520
([(0,3),(1,4),(2,5),(3,5),(4,2)],6) generating graphics... => 521
([(0,4),(0,5),(3,2),(4,3),(5,1)],6) generating graphics... => 521
([(0,5),(1,4),(4,2),(4,5),(5,3)],6) generating graphics... => 523
([(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 523
([(0,4),(0,5),(1,2),(1,4),(1,5),(4,3),(5,3)],6) generating graphics... => 523
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6) generating graphics... => 524
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6) generating graphics... => 524
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) generating graphics... => 528
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) generating graphics... => 528
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) generating graphics... => 529
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) generating graphics... => 529
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) generating graphics... => 533
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) generating graphics... => 533
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) generating graphics... => 533
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 533
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) generating graphics... => 538
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) generating graphics... => 538
([(0,4),(3,5),(4,3),(5,1),(5,2)],6) generating graphics... => 546
([(0,5),(1,5),(3,2),(4,3),(5,4)],6) generating graphics... => 546
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) generating graphics... => 550
([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6) generating graphics... => 552
([(0,4),(1,5),(5,2),(5,3)],6) generating graphics... => 552
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) generating graphics... => 552
([(0,5),(1,5),(2,3),(5,4)],6) generating graphics... => 552
([(0,5),(1,2),(2,5),(5,3),(5,4)],6) generating graphics... => 555
([(0,5),(1,5),(4,2),(5,3),(5,4)],6) generating graphics... => 555
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) generating graphics... => 556
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) generating graphics... => 556
([(0,5),(1,5),(2,3),(2,4),(2,5)],6) generating graphics... => 560
([(0,5),(1,4),(1,5),(4,2),(4,3)],6) generating graphics... => 561
([(0,4),(1,4),(2,3),(2,5),(4,5)],6) generating graphics... => 561
([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6) generating graphics... => 562
([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6) generating graphics... => 562
([(0,5),(1,3),(3,4),(4,2),(4,5)],6) generating graphics... => 571
([(0,5),(1,3),(1,5),(4,2),(5,4)],6) generating graphics... => 571
([(0,5),(1,5),(4,2),(4,3),(5,4)],6) generating graphics... => 573
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) generating graphics... => 579
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6) generating graphics... => 579
([(0,5),(1,2),(1,3),(3,5),(5,4)],6) generating graphics... => 581
([(0,5),(1,4),(3,5),(4,2),(4,3)],6) generating graphics... => 581
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) generating graphics... => 586
([(0,4),(3,2),(4,5),(5,1),(5,3)],6) generating graphics... => 586
([(0,5),(1,3),(3,5),(4,2),(5,4)],6) generating graphics... => 586
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 586
([(0,4),(1,3),(3,5),(4,5),(5,2)],6) generating graphics... => 593
([(0,5),(3,2),(4,1),(5,3),(5,4)],6) generating graphics... => 593
([(1,4),(1,5),(2,3),(2,5)],6) generating graphics... => 600
([(1,5),(2,4),(3,4),(3,5)],6) generating graphics... => 600
([(0,5),(1,2),(1,4),(3,5),(4,3)],6) generating graphics... => 603
([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6) generating graphics... => 605
([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6) generating graphics... => 605
([(0,5),(3,4),(4,2),(5,1),(5,3)],6) generating graphics... => 606
([(0,5),(1,4),(2,5),(4,2),(5,3)],6) generating graphics... => 606
([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) generating graphics... => 610
([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) generating graphics... => 610
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) generating graphics... => 611
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6) generating graphics... => 611
([(0,5),(1,3),(1,4),(1,5),(4,2)],6) generating graphics... => 612
([(0,5),(1,4),(2,3),(2,5),(4,5)],6) generating graphics... => 612
([(0,5),(1,3),(1,4),(4,2),(4,5)],6) generating graphics... => 619
([(0,5),(1,4),(2,3),(2,4),(4,5)],6) generating graphics... => 619
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) generating graphics... => 626
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) generating graphics... => 626
([(0,5),(1,2),(1,5),(5,3),(5,4)],6) generating graphics... => 629
([(0,5),(1,5),(2,4),(5,3),(5,4)],6) generating graphics... => 629
([(1,4),(2,3),(2,5),(4,5)],6) generating graphics... => 636
([(1,5),(2,3),(2,5),(3,4)],6) generating graphics... => 636
([(0,5),(1,2),(1,3),(1,5),(5,4)],6) generating graphics... => 640
([(0,5),(1,5),(2,3),(3,4),(3,5)],6) generating graphics... => 640
([(0,5),(1,4),(2,5),(3,2),(4,3)],6) generating graphics... => 641
([(0,2),(0,5),(3,4),(4,1),(5,3)],6) generating graphics... => 641
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) generating graphics... => 646
([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5)],6) generating graphics... => 650
([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6) generating graphics... => 650
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) generating graphics... => 650
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 650
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) generating graphics... => 650
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) generating graphics... => 650
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6) generating graphics... => 652
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 652
([(1,4),(1,5),(2,3),(2,4),(3,5)],6) generating graphics... => 660
([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6) generating graphics... => 662
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) generating graphics... => 680
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6) generating graphics... => 680
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6) generating graphics... => 692
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 692
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) generating graphics... => 693
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) generating graphics... => 693
([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) generating graphics... => 700
([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6) generating graphics... => 700
([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) generating graphics... => 704
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) generating graphics... => 704
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) generating graphics... => 704
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6) generating graphics... => 704
([(0,5),(1,2),(1,3),(1,4),(4,5)],6) generating graphics... => 709
([(0,5),(1,5),(2,3),(2,4),(4,5)],6) generating graphics... => 709
([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6) generating graphics... => 717
([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6) generating graphics... => 717
([(0,5),(1,4),(2,3)],6) generating graphics... => 729
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) generating graphics... => 737
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) generating graphics... => 737
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6) generating graphics... => 745
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6) generating graphics... => 745
([(0,5),(1,2),(1,3),(1,4)],6) generating graphics... => 760
([(0,5),(1,5),(2,5),(3,4)],6) generating graphics... => 760
([(1,5),(3,4),(4,2),(5,3)],6) generating graphics... => 762
([(0,5),(1,4),(4,2),(4,3),(4,5)],6) generating graphics... => 763
([(0,5),(1,5),(2,3),(2,5),(5,4)],6) generating graphics... => 763
([(1,5),(2,3),(2,4),(4,5)],6) generating graphics... => 774
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6) generating graphics... => 774
([(1,5),(2,3),(3,4),(3,5)],6) generating graphics... => 780
([(1,5),(2,3),(2,5),(5,4)],6) generating graphics... => 780
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 783
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 783
([(1,4),(1,5),(2,3),(3,4),(3,5)],6) generating graphics... => 786
([(1,4),(1,5),(2,4),(2,5),(5,3)],6) generating graphics... => 786
([(0,4),(0,5),(4,3),(5,1),(5,2)],6) generating graphics... => 801
([(0,4),(1,4),(2,3),(3,5),(4,5)],6) generating graphics... => 801
([(1,2),(1,3),(2,5),(3,5),(5,4)],6) generating graphics... => 804
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 804
([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 804
([(1,4),(2,5),(3,5),(4,2),(4,3)],6) generating graphics... => 804
([(1,3),(1,4),(3,5),(4,2),(4,5)],6) generating graphics... => 816
([(1,4),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 816
([(1,3),(1,4),(2,5),(3,5),(4,2)],6) generating graphics... => 822
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) generating graphics... => 824
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) generating graphics... => 824
([(0,5),(1,4),(2,4),(3,5),(4,3)],6) generating graphics... => 832
([(0,3),(0,4),(4,5),(5,1),(5,2)],6) generating graphics... => 832
([(1,4),(2,3),(3,5),(4,5)],6) generating graphics... => 852
([(1,4),(1,5),(4,3),(5,2)],6) generating graphics... => 852
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 868
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) generating graphics... => 868
([(0,5),(1,5),(5,2),(5,3),(5,4)],6) generating graphics... => 874
([(0,5),(1,5),(2,5),(5,3),(5,4)],6) generating graphics... => 874
([(1,4),(1,5),(2,3),(2,4),(2,5)],6) generating graphics... => 876
([(1,5),(2,5),(5,3),(5,4)],6) generating graphics... => 876
([(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 876
([(1,4),(4,5),(5,2),(5,3)],6) generating graphics... => 888
([(1,5),(2,5),(3,4),(5,3)],6) generating graphics... => 888
([(1,3),(2,4),(4,5)],6) generating graphics... => 900
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6) generating graphics... => 901
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6) generating graphics... => 901
([(1,5),(2,3),(2,4),(2,5)],6) generating graphics... => 912
([(1,5),(2,5),(3,4),(3,5)],6) generating graphics... => 912
([(0,5),(4,2),(4,3),(5,1),(5,4)],6) generating graphics... => 918
([(1,5),(2,5),(3,4)],6) generating graphics... => 918
([(1,5),(2,3),(2,4)],6) generating graphics... => 918
([(0,5),(1,4),(2,4),(4,5),(5,3)],6) generating graphics... => 918
([(1,5),(2,3),(3,5),(5,4)],6) generating graphics... => 930
([(1,5),(4,3),(5,2),(5,4)],6) generating graphics... => 930
([(1,3),(1,5),(4,2),(5,4)],6) generating graphics... => 936
([(1,5),(2,3),(3,4),(4,5)],6) generating graphics... => 936
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) generating graphics... => 951
([(0,3),(0,5),(4,2),(5,1),(5,4)],6) generating graphics... => 963
([(0,5),(1,4),(2,3),(3,5),(5,4)],6) generating graphics... => 963
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) generating graphics... => 970
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 970
([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) generating graphics... => 1004
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) generating graphics... => 1004
([(0,4),(4,5),(5,1),(5,2),(5,3)],6) generating graphics... => 1005
([(0,5),(1,5),(2,5),(3,4),(5,3)],6) generating graphics... => 1005
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 1008
([(1,2),(1,3),(1,4),(3,5),(4,5)],6) generating graphics... => 1008
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) generating graphics... => 1045
([(0,2),(0,3),(0,5),(4,1),(5,4)],6) generating graphics... => 1045
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) generating graphics... => 1053
([(0,3),(0,4),(0,5),(4,2),(5,1)],6) generating graphics... => 1053
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) generating graphics... => 1074
([(0,5),(4,3),(5,1),(5,2),(5,4)],6) generating graphics... => 1122
([(0,5),(1,5),(2,3),(3,5),(5,4)],6) generating graphics... => 1122
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) generating graphics... => 1167
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 1167
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) generating graphics... => 1188
([(2,5),(3,4),(3,5)],6) generating graphics... => 1188
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 1188
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) generating graphics... => 1231
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 1231
([(0,5),(1,2),(1,3),(1,4),(1,5)],6) generating graphics... => 1291
([(0,5),(1,5),(2,5),(3,4),(3,5)],6) generating graphics... => 1291
([(1,4),(1,5),(5,2),(5,3)],6) generating graphics... => 1332
([(2,3),(3,5),(5,4)],6) generating graphics... => 1332
([(1,5),(2,4),(3,4),(4,5)],6) generating graphics... => 1332
([(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 1368
([(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 1368
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) generating graphics... => 1430
([(2,5),(3,4),(4,5)],6) generating graphics... => 1512
([(2,3),(2,4),(4,5)],6) generating graphics... => 1512
([(2,3),(3,4),(3,5)],6) generating graphics... => 1512
([(2,5),(3,5),(5,4)],6) generating graphics... => 1512
([(1,5),(5,2),(5,3),(5,4)],6) generating graphics... => 1578
([(1,5),(2,5),(3,5),(5,4)],6) generating graphics... => 1578
([(1,3),(1,4),(1,5),(5,2)],6) generating graphics... => 1596
([(1,5),(2,5),(3,4),(4,5)],6) generating graphics... => 1596
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) generating graphics... => 1782
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 1782
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) generating graphics... => 1867
([(0,3),(0,4),(0,5),(5,1),(5,2)],6) generating graphics... => 1867
([(0,4),(0,5),(5,1),(5,2),(5,3)],6) generating graphics... => 1976
([(0,5),(1,5),(2,5),(3,4),(5,4)],6) generating graphics... => 1976
([(2,5),(3,4)],6) generating graphics... => 2304
([(2,5),(3,5),(4,5)],6) generating graphics... => 2484
([(2,3),(2,4),(2,5)],6) generating graphics... => 2484
([(0,5),(5,1),(5,2),(5,3),(5,4)],6) generating graphics... => 2558
([(0,5),(1,5),(2,5),(3,5),(5,4)],6) generating graphics... => 2558
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) generating graphics... => 2620
([(0,2),(0,3),(0,4),(0,5),(5,1)],6) generating graphics... => 2620
([(3,4),(4,5)],6) generating graphics... => 2808
([(3,5),(4,5)],6) generating graphics... => 3024
([(3,4),(3,5)],6) generating graphics... => 3024
([(1,5),(2,5),(3,5),(4,5)],6) generating graphics... => 3780
([(1,2),(1,3),(1,4),(1,5)],6) generating graphics... => 3780
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) generating graphics... => 7781
([(0,1),(0,2),(0,3),(0,4),(0,5)],6) generating graphics... => 7781
([(4,5)],6) generating graphics... => 9072
([],6) generating graphics... => 46656
click to show generating function       
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):
    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
Oct 26, 2016 at 15:11 by Wilberd van der Kallen