Identifier
-
Mp00251:
Graphs
—clique sizes⟶
Integer partitions
St000812: Integer partitions ⟶ ℤ
Values
([],1) => [1] => 1
([],2) => [1,1] => 3
([(0,1)],2) => [2] => 2
([],3) => [1,1,1] => 10
([(1,2)],3) => [2,1] => 6
([(0,2),(1,2)],3) => [2,2] => 16
([(0,1),(0,2),(1,2)],3) => [3] => 3
([],4) => [1,1,1,1] => 47
([(2,3)],4) => [2,1,1] => 27
([(1,3),(2,3)],4) => [2,2,1] => 76
([(0,3),(1,3),(2,3)],4) => [2,2,2] => 263
([(0,3),(1,2)],4) => [2,2] => 16
([(0,3),(1,2),(2,3)],4) => [2,2,2] => 263
([(1,2),(1,3),(2,3)],4) => [3,1] => 12
([(0,3),(1,2),(1,3),(2,3)],4) => [3,2] => 32
([(0,2),(0,3),(1,2),(1,3)],4) => [2,2,2,2] => 7548
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [3,3] => 79
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [4] => 5
([],5) => [1,1,1,1,1] => 246
([(3,4)],5) => [2,1,1,1] => 136
([(2,4),(3,4)],5) => [2,2,1,1] => 476
([(1,4),(2,4),(3,4)],5) => [2,2,2,1] => 1765
([(0,4),(1,4),(2,4),(3,4)],5) => [2,2,2,2] => 7548
([(1,4),(2,3)],5) => [2,2,1] => 76
([(1,4),(2,3),(3,4)],5) => [2,2,2,1] => 1765
([(0,1),(2,4),(3,4)],5) => [2,2,2] => 263
([(2,3),(2,4),(3,4)],5) => [3,1,1] => 56
([(0,4),(1,4),(2,3),(3,4)],5) => [2,2,2,2] => 7548
([(1,4),(2,3),(2,4),(3,4)],5) => [3,2,1] => 191
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => [3,2,2] => 685
([(1,3),(1,4),(2,3),(2,4)],5) => [2,2,2,2,1] => 65786
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [2,2,2,2,2] => 339857
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [3,3,1] => 493
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => [3,2,2] => 685
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [3,3,2] => 2041
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => [2,2,2,2,2,2] => 22190989
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [3,3,3] => 6417
([(0,4),(1,3),(2,3),(2,4)],5) => [2,2,2,2] => 7548
([(0,1),(2,3),(2,4),(3,4)],5) => [3,2] => 32
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => [3,2,2] => 685
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => [3,3] => 79
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => [2,2,2,2,2] => 339857
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => [3,2,2,2] => 24339
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => [3,3,3] => 6417
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => [3,3,2] => 2041
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [4,1] => 20
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [4,2] => 65
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [4,3] => 160
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => [3,3,2,2] => 86494
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => [3,3,3,3] => 1342215
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [4,4] => 371
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5] => 7
([],6) => [1,1,1,1,1,1] => 1602
([(4,5)],6) => [2,1,1,1,1] => 870
([(3,5),(4,5)],6) => [2,2,1,1,1] => 3280
([(2,5),(3,5),(4,5)],6) => [2,2,2,1,1] => 14162
([(1,5),(2,5),(3,5),(4,5)],6) => [2,2,2,2,1] => 65786
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [2,2,2,2,2] => 339857
([(2,5),(3,4)],6) => [2,2,1,1] => 476
([(2,5),(3,4),(4,5)],6) => [2,2,2,1,1] => 14162
([(1,2),(3,5),(4,5)],6) => [2,2,2,1] => 1765
([(3,4),(3,5),(4,5)],6) => [3,1,1,1] => 344
([(1,5),(2,5),(3,4),(4,5)],6) => [2,2,2,2,1] => 65786
([(0,1),(2,5),(3,5),(4,5)],6) => [2,2,2,2] => 7548
([(2,5),(3,4),(3,5),(4,5)],6) => [3,2,1,1] => 1261
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [2,2,2,2,2] => 339857
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [3,2,2,1] => 5342
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [3,2,2,2] => 24339
([(2,4),(2,5),(3,4),(3,5)],6) => [2,2,2,2,1,1] => 650606
([(0,5),(1,5),(2,4),(3,4)],6) => [2,2,2,2] => 7548
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [2,2,2,2,2,1] => 3637109
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [2,2,2,2,2] => 339857
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,1,1] => 3790
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,2,2,1] => 5342
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [2,2,2,2,2] => 339857
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [2,2,2,2,2,2] => 22190989
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2,1] => 17109
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,2,2,2] => 24339
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2,2] => 86494
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [2,2,2,2,2,2,1] => 282002663
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => [2,2,2,2,2,2] => 22190989
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,1] => 60442
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2,2] => 86494
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,2] => 326656
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,3] => 1342215
([(0,5),(1,4),(2,3)],6) => [2,2,2] => 263
([(1,5),(2,4),(3,4),(3,5)],6) => [2,2,2,2,1] => 65786
([(0,1),(2,5),(3,4),(4,5)],6) => [2,2,2,2] => 7548
([(1,2),(3,4),(3,5),(4,5)],6) => [3,2,1] => 191
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [2,2,2,2,2] => 339857
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => [3,2,2,1] => 5342
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => [3,2,2] => 685
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [3,2,2,2] => 24339
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [3,3,1] => 493
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [3,3,2] => 2041
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => [2,2,2,2,2,1] => 3637109
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [2,2,2,2,2,2] => 22190989
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,2,2,2,1] => 236463
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => [2,2,2,2,2,2] => 22190989
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [3,3,2,1] => 17109
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => [3,2,2,2] => 24339
>>> Load all 628 entries. <<<([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,2,2,2,2] => 1305408
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2,2] => 86494
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,1] => 60442
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,2] => 326656
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [2,2,2,2,2] => 339857
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [2,2,2,2,2] => 339857
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => [3,2,2] => 685
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => [2,2,2,2,2,2] => 22190989
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => [3,2,2,2] => 24339
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => [3,2,2,2] => 24339
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2] => 2041
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => [3,2,2,2] => 24339
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => [3,2,2,2,2] => 1305408
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => [3,3,2,2] => 86494
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2] => 2041
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3] => 6417
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,1,1] => 114
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [3,3,2,2] => 86494
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2,1] => 398
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2,2] => 1632
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) => [3,2,2,2,2,2] => 99245511
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,2] => 326656
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [3,3,3,2] => 326656
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2,2,2] => 5435521
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,3] => 1342215
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [3,3,2,2,2] => 5435521
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,1] => 1167
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2,2] => 1632
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,2] => 5090
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,3] => 17617
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [3,3,2,2,1] => 903777
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [3,3,2,2,2] => 5435521
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [3,3,3,3,1] => 16505959
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => [2,2,2,2,2,2] => 22190989
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => [3,2,2,2,2] => 1305408
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,2,2,2,2] => 1305408
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [3,3,2,2] => 86494
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => [3,2,2,2,2] => 1305408
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2,2,2] => 5435521
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [3,3,3,2] => 326656
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [3,3,2,2] => 86494
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [3,3,3,3] => 1342215
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [3,3,2,2,2] => 5435521
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,2,2] => 24033962
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4,1] => 2872
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,2] => 5090
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4,2] => 13905
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,2,2] => 24033962
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [3,3,3,3] => 1342215
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,3] => 17617
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4,3] => 50801
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4,4] => 158810
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => [3,3] => 79
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => [3,3,2,2] => 86494
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => [3,3,2] => 2041
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2] => 65
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [3,3,3] => 6417
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2,2] => 1632
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3] => 160
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => [3,3,2,2] => 86494
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => [3,3,3,2] => 326656
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,2] => 5090
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,3] => 1342215
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2,2,2] => 67880
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,3] => 17617
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [3,3,3,3] => 1342215
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4] => 371
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6) => [3,2,2,2,2,2] => 99245511
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [3,3,2,2,2] => 5435521
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [3,3,3,2,2] => 24033962
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => [3,3,2,2,2] => 5435521
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,3,3] => 4532834
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4,4] => 158810
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [4,3,2,2] => 254989
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,3] => 17617
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4,3] => 50801
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4,2] => 13905
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1] => 35
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,2] => 113
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,3] => 318
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,4] => 756
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [4,4,2,2] => 811289
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,3,2] => 1043121
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,5] => 1683
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 11
([],7) => [1,1,1,1,1,1,1] => 11481
([(5,6)],7) => [2,1,1,1,1,1] => 6124
([(4,6),(5,6)],7) => [2,2,1,1,1,1] => 26673
([(3,6),(4,6),(5,6)],7) => [2,2,2,1,1,1] => 125088
([(2,6),(3,6),(4,6),(5,6)],7) => [2,2,2,2,1,1] => 650606
([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [2,2,2,2,2,1] => 3637109
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [2,2,2,2,2,2] => 22190989
([(3,6),(4,5)],7) => [2,2,1,1,1] => 3280
([(3,6),(4,5),(5,6)],7) => [2,2,2,1,1,1] => 125088
([(2,3),(4,6),(5,6)],7) => [2,2,2,1,1] => 14162
([(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 2335
([(2,6),(3,6),(4,5),(5,6)],7) => [2,2,2,2,1,1] => 650606
([(1,2),(3,6),(4,6),(5,6)],7) => [2,2,2,2,1] => 65786
([(3,6),(4,5),(4,6),(5,6)],7) => [3,2,1,1,1] => 9997
([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [2,2,2,2,2,1] => 3637109
([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => [2,2,2,2,2] => 339857
([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,1,1] => 46068
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [2,2,2,2,2,2] => 22190989
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,1] => 236463
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => 1305408
([(3,5),(3,6),(4,5),(4,6)],7) => [2,2,2,2,1,1,1] => 7017789
([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,2,2,1] => 65786
([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [2,2,2,2,2,1,1] => 43012769
([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [2,2,2,2,2,1] => 3637109
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [2,2,2,2,2] => 339857
([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,1,1,1] => 32313
([(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,1,1] => 46068
([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [2,2,2,2,2,1] => 3637109
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [2,2,2,2,2,2,1] => 282002663
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [2,2,2,2,2,2] => 22190989
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,1,1] => 164735
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,1] => 236463
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [2,2,2,2,2,2] => 22190989
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,1] => 903777
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => 1305408
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => 5435521
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,2,2,2,2,1] => 282002663
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [2,2,2,2,2,2] => 22190989
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,1,1] => 626353
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,1] => 903777
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => 1305408
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,1] => 3747889
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => 5435521
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,1] => 16505959
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(1,6),(2,5),(3,4)],7) => [2,2,2,1] => 1765
([(2,6),(3,5),(4,5),(4,6)],7) => [2,2,2,2,1,1] => 650606
([(1,2),(3,6),(4,5),(5,6)],7) => [2,2,2,2,1] => 65786
([(0,3),(1,2),(4,6),(5,6)],7) => [2,2,2,2] => 7548
([(2,3),(4,5),(4,6),(5,6)],7) => [3,2,1,1] => 1261
([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [2,2,2,2,2,1] => 3637109
([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [2,2,2,2,2] => 339857
([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,2,2,1,1] => 46068
([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,1] => 5342
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [2,2,2,2,2,2] => 22190989
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,2,2,2,1] => 236463
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2] => 24339
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,1,1] => 3790
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => 1305408
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,2,1] => 17109
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,2,2] => 86494
([(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [2,2,2,2,2,1,1] => 43012769
([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [2,2,2,2,2,2,1] => 282002663
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [2,2,2,2,2,2] => 22190989
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,1,1] => 2512916
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7) => [2,2,2,2,2,2,1] => 282002663
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,1,1] => 164735
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [3,2,2,2,1] => 236463
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,1] => 15264278
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => 1305408
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,1] => 903777
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => 1305408
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,1,1] => 626353
([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => 99245511
([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => 5435521
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,1] => 3747889
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [2,2,2,2,2,1] => 3637109
([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,2,2,2,1] => 3637109
([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [2,2,2,2,2] => 339857
([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,2,2,1] => 5342
([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [2,2,2,2,2,2,1] => 282002663
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [2,2,2,2,2,2] => 22190989
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,2,2,2,2] => 22190989
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7) => [3,2,2,2,1] => 236463
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [3,2,2,2] => 24339
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,1] => 236463
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,1] => 17109
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [2,2,2,2,2,2] => 22190989
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2] => 24339
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,2,2,2,1] => 236463
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2,1] => 15264278
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7) => [3,2,2,2,2] => 1305408
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,1] => 903777
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => 1305408
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2] => 86494
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,1] => 17109
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2] => 1305408
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2,2] => 99245511
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2] => 5435521
([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,1] => 60442
([(0,6),(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2] => 86494
([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => 326656
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,2,2,2] => 24339
([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => 727
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,2,2,2,2] => 1305408
([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2,1] => 903777
([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,1,1] => 3021
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => 5435521
([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,1] => 13520
([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => 67880
([(0,6),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [3,2,2,2,2,2] => 99245511
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,1] => 3747889
([(0,6),(1,5),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => 5435521
([(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,2,1] => 3747889
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2,1] => 68029106
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => 5435521
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => 99245511
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,1] => 16505959
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7) => [3,2,2,2,2] => 1305408
([(0,5),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,2,2,2,2,2] => 99245511
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [3,3,2,2,2] => 5435521
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => 326656
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2] => 86494
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,5),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => 326656
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3] => 1342215
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7) => [3,2,2,2,2,2] => 99245511
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2,1] => 68029106
([(0,6),(1,6),(2,3),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => 5435521
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,1,1] => 9537
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,1] => 13520
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,1] => 47494
([(0,6),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => 67880
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => 254989
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,1] => 177326
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => 254989
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => 1043121
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,3] => 4532834
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,1,1] => 10507313
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2,1] => 68029106
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => 99245511
([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7) => [2,2,2,2,2,2,1] => 282002663
([(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,1] => 15264278
([(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,1] => 15264278
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,1] => 903777
([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [3,2,2,2,2,1] => 15264278
([(1,2),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2,1] => 68029106
([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => 5435521
([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => 99245511
([(0,6),(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => 99245511
([(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2,1] => 3747889
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,2,2,1] => 903777
([(0,6),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => 5435521
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => 99245511
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,3,1] => 16505959
([(0,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,2,2,2] => 5435521
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [2,2,2,2,2,2] => 22190989
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => [3,3,2,2] => 86494
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7) => [3,2,2,2,2] => 1305408
([(0,4),(1,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2] => 1305408
([(0,4),(1,4),(1,6),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => [3,3,2,2,2] => 5435521
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => 99245511
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2] => 5435521
([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2] => 86494
([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,3,2] => 326656
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,3,3] => 1342215
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,2,2,2,1] => 68029106
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5)],7) => [3,2,2,2,2,2] => 99245511
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,5),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,1,1] => 26220
([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,1] => 138695
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => 254989
([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,2] => 811289
([(0,5),(1,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,2,2,2] => 5435521
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,1] => 47494
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,3,1] => 16505959
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => 67880
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,1] => 177326
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => 254989
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => 1043121
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,6),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,1] => 561917
([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,2] => 811289
([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,2] => 3510016
([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => 1043121
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => 1043121
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,3] => 4532834
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,4,1] => 1875822
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,2] => 3510016
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,3] => 4532834
([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [2,2,2,2,2] => 339857
([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => [3,2,2] => 685
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [2,2,2,2,2,2] => 22190989
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2] => 24339
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2] => 1305408
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,2] => 2041
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,3,2,2] => 86494
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,3,3] => 6417
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [2,2,2,2,2,2] => 22190989
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [2,2,2,2,2,2] => 22190989
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7) => [3,2,2,2] => 24339
([(0,4),(1,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7) => [3,2,2,2,2] => 1305408
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => 1305408
([(0,6),(1,4),(2,3),(2,5),(3,5),(4,6),(5,6)],7) => [3,2,2,2,2] => 1305408
([(0,5),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6)],7) => [3,2,2,2,2] => 1305408
([(0,5),(1,4),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => 1305408
([(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2,2] => 99245511
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => [3,2,2,2,2,2] => 99245511
([(0,4),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [3,3,2,2] => 86494
([(0,1),(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2,2] => 99245511
([(0,4),(1,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => 5435521
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => 326656
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2] => 86494
([(0,1),(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => 5435521
([(0,3),(1,5),(1,6),(2,4),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => 326656
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3] => 1342215
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => [3,3,1] => 493
([(1,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) => [3,3,2,2,1] => 903777
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2] => 86494
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,2,1] => 17109
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [3,3,2] => 2041
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,1] => 398
([(0,6),(1,2),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => 5435521
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,2,2] => 86494
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,1] => 60442
([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,1] => 13520
([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2] => 1632
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => 326656
([(0,6),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => 67880
([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,1] => 1167
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2] => 5090
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2] => 5435521
([(0,4),(1,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,5),(1,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,3),(1,5),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => 99245511
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7) => [3,3,2,2,1] => 903777
([(0,6),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,2,2,2] => 5435521
([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,3,2,1] => 3747889
([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,1] => 47494
([(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,1] => 16505959
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2,1] => 704026
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => 254989
([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,1] => 177326
([(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2,2] => 4214013
([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => 1043121
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7) => [3,3,2,2] => 86494
([(0,1),(0,6),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,2,2,2] => 5435521
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,3,2] => 326656
([(0,5),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => 67880
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2] => 5090
([(0,6),(1,2),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => 326656
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3] => 6417
([(0,1),(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,2),(1,5),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => 254989
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,3] => 1342215
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2] => 5090
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3] => 17617
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,3,2,2] => 24033962
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => 1043121
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => 1043121
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,3] => 4532834
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,3,3,1] => 16505959
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,1] => 2872
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2] => 13905
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3] => 50801
([(0,3),(1,4),(1,5),(2,4),(2,6),(3,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => 99245511
([(0,1),(0,3),(1,2),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => 99245511
([(0,6),(1,2),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2] => 5435521
([(0,6),(1,2),(1,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => 99245511
([(0,3),(1,2),(1,5),(2,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => 99245511
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7) => [3,2,2,2,2,2] => 99245511
([(0,6),(1,2),(1,6),(2,4),(3,4),(3,5),(4,5),(5,6)],7) => [3,2,2,2,2,2] => 99245511
([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,5),(1,3),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2] => 5435521
([(0,1),(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2] => 5435521
([(0,5),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,4),(0,6),(1,3),(1,6),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2,1] => 68029106
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [3,3,2,2,2,1] => 68029106
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,1] => 138695
([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => 254989
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,1] => 177326
([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [4,3,2,2,1] => 2907772
([(0,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,2] => 811289
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,1] => 561917
([(0,6),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => 1043121
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,2] => 3510016
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => 1043121
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,3] => 4532834
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,2] => 3510016
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,2] => 3510016
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,3] => 4532834
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,4,1] => 1875822
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2,2] => 99245511
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2] => 5435521
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => 5435521
([(0,1),(0,6),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [3,3,2,2,2] => 5435521
([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => [3,3,2,2,2] => 5435521
([(0,3),(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,4),(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,1),(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => 254989
([(0,1),(0,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2,2] => 4214013
([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [4,3,3,2] => 1043121
([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [4,3,2,2] => 254989
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [4,3,3,3] => 4532834
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,3,2] => 326656
([(0,3),(0,6),(1,3),(1,5),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,6),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => 254989
([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2,2] => 4214013
([(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => 1043121
([(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => 1043121
([(0,4),(0,6),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,3] => 4532834
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,1),(0,5),(1,5),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3] => 1342215
([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => 254989
([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2] => 13905
([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3] => 1342215
([(0,1),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,2] => 811289
([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3] => 17617
([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3] => 50801
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,4),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [4,2,2,2,2] => 4214013
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => 254989
([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => 1043121
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,3] => 4532834
([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,2] => 3510016
([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,3] => 4532834
([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2] => 13905
([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,3] => 4532834
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3] => 50801
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,4] => 158810
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7) => [3,2,2,2,2] => 1305408
([(0,3),(1,3),(1,4),(2,5),(2,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => 5435521
([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2] => 1632
([(0,6),(1,2),(1,4),(2,4),(3,5),(3,6),(4,5),(5,6)],7) => [3,3,2,2] => 86494
([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3] => 6417
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5)],7) => [3,3,2,2,2] => 5435521
([(0,2),(1,2),(1,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => 67880
([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2] => 326656
([(0,5),(1,3),(1,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,3,2] => 326656
([(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [4,2,2,2] => 67880
([(0,1),(0,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2,2] => 4214013
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3] => 1342215
([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [4,3,2] => 5090
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [4,3,3] => 17617
([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 202
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,2] => 811289
([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,2,1] => 800
([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,2,2] => 3423
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,3] => 4532834
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,2] => 3510016
([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,1] => 2435
([(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,2,2] => 3423
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,2] => 11694
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,3] => 42473
([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2,1] => 12756465
([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [4,4,2,2,1] => 9864237
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,3,3] => 1342215
([(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [4,4,2,2] => 811289
([(0,5),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [4,4,3,2] => 3510016
([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,1] => 6539
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,2] => 11694
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,2] => 33373
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,3] => 42473
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,3] => 132211
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,4] => 433217
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,3),(0,4),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,2] => 811289
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,5,1] => 15469
([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,2] => 33373
([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,5,2] => 86219
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,3] => 42473
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,3] => 132211
([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,5,3] => 359371
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,4] => 433217
([(0,4),(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5)],7) => [3,3,3,2] => 326656
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3] => 160
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3] => 1342215
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [4,3,2] => 5090
([(0,4),(0,5),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3] => 17617
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [4,4] => 371
([(0,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => 1043121
([(0,3),(0,6),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => 1043121
([(0,4),(0,5),(1,2),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,3] => 4532834
([(0,2),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,2] => 3510016
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(3,6),(4,5),(5,6)],7) => [3,3,3,2,2] => 24033962
([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => [4,3,2,2] => 254989
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [4,3,3] => 17617
([(0,1),(0,2),(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => 1043121
([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,3] => 4532834
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3] => 50801
([(0,1),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,2] => 811289
([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,2] => 113
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3] => 50801
([(0,1),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,2,2] => 3423
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3] => 318
([(0,1),(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [4,3,3,3] => 4532834
([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3] => 50801
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,4] => 158810
([(0,1),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [4,4,3,2] => 3510016
([(0,1),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,2] => 11694
([(0,1),(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,2,2,2] => 166038
([(0,1),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,3] => 42473
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4] => 756
([(0,2),(0,6),(1,3),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [4,3,3,2] => 1043121
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [4,3,3,3] => 4532834
([(0,2),(0,3),(0,4),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,2] => 3510016
([(0,3),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,2] => 33373
([(0,1),(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,2,2] => 673104
([(0,3),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,3] => 132211
([(0,3),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,4] => 433217
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,5] => 1683
([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,3,3,2] => 2899935
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,4] => 433217
([(0,2),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,2,2] => 2248291
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,4,3] => 132211
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,5,3] => 359371
([(0,6),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,5,2] => 86219
([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 54
([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,2] => 199
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,3] => 573
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,4] => 1485
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,5] => 3405
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,6] => 7413
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 15
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,0,0,1,0,0,0,1,0,0,0,0,0,1
$F_{1} = q$
$F_{2} = q^{2} + q^{3}$
$F_{3} = q^{3} + q^{6} + q^{10} + q^{16}$
$F_{4} = q^{5} + q^{12} + q^{16} + q^{27} + q^{32} + q^{47} + q^{76} + q^{79} + 2\ q^{263} + q^{7548}$
$F_{5} = q^{7} + q^{20} + q^{32} + q^{56} + q^{65} + q^{76} + q^{79} + q^{136} + q^{160} + q^{191} + q^{246} + q^{263} + q^{371} + q^{476} + q^{493} + 3\ q^{685} + 2\ q^{1765} + 2\ q^{2041} + 2\ q^{6417} + 3\ q^{7548} + q^{24339} + q^{65786} + q^{86494} + 2\ q^{339857} + q^{1342215} + q^{22190989}$
Description
The sum of the entries in the column specified by the partition of the change of basis matrix from complete homogeneous symmetric functions to monomial symmetric functions.
For example, $h_{11} = 2m_{11} + m_2$, so the statistic on the partition $11$ is 3.
For example, $h_{11} = 2m_{11} + m_2$, so the statistic on the partition $11$ is 3.
Map
clique sizes
Description
The integer partition of the sizes of the maximal cliques of a graph.
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