Identifier
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
Images
[(1,2)] => [2,1] => ([(0,1)],2)
[(1,2),(3,4)] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[(1,3),(2,4)] => [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
[(1,4),(2,3)] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(1,12),(2,6),(2,7),(2,12),(3,5),(3,7),(3,12),(5,9),(5,10),(6,9),(6,11),(7,9),(7,10),(7,11),(8,4),(9,13),(10,8),(10,13),(11,8),(11,13),(12,10),(12,11),(13,4)],14)
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => ([(0,2),(0,3),(0,4),(1,7),(1,8),(2,1),(2,11),(2,12),(3,9),(3,10),(3,12),(4,9),(4,10),(4,11),(5,15),(5,16),(7,15),(7,16),(8,15),(8,16),(9,5),(9,13),(10,5),(10,14),(11,7),(11,13),(11,14),(12,8),(12,13),(12,14),(13,16),(14,15),(14,16),(15,6),(16,6)],17)
[(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => ([(0,4),(0,5),(1,7),(2,9),(2,11),(3,2),(3,10),(4,3),(4,6),(5,1),(5,6),(6,7),(6,10),(7,11),(9,8),(10,9),(10,11),(11,8)],12)
[(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,18),(1,19),(2,7),(2,13),(2,15),(3,7),(3,12),(3,15),(4,8),(4,9),(4,12),(4,15),(5,8),(5,10),(5,13),(5,15),(6,1),(6,9),(6,10),(6,12),(6,13),(7,17),(8,14),(8,21),(9,14),(9,18),(9,19),(9,21),(10,14),(10,18),(10,19),(10,21),(12,17),(12,18),(12,21),(13,17),(13,19),(13,21),(14,16),(14,20),(15,17),(15,21),(16,11),(17,20),(18,16),(18,20),(19,16),(19,20),(20,11),(21,16),(21,20)],22)
[(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(1,11),(1,12),(2,8),(2,9),(2,12),(3,5),(3,7),(3,9),(3,11),(4,5),(4,7),(4,8),(4,10),(5,19),(7,13),(7,14),(7,19),(8,13),(8,15),(8,19),(9,13),(9,16),(9,19),(10,14),(10,15),(10,19),(11,14),(11,16),(11,19),(12,15),(12,16),(13,17),(13,18),(14,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,6),(18,6),(19,18)],20)
[(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,15),(2,7),(2,9),(2,15),(3,6),(3,7),(3,15),(4,6),(4,8),(4,15),(6,14),(7,11),(7,14),(8,12),(8,14),(9,11),(9,12),(10,5),(11,10),(11,13),(12,10),(12,13),(13,5),(14,13),(15,11),(15,12),(15,14)],16)
[(1,5),(2,4),(3,6)] => [5,4,6,2,1,3] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(1,10),(1,12),(2,8),(2,10),(2,11),(3,7),(3,8),(3,12),(4,7),(4,9),(4,11),(5,15),(5,16),(7,17),(8,13),(8,17),(9,14),(9,17),(10,13),(10,14),(11,5),(11,14),(11,17),(12,5),(12,13),(12,17),(13,15),(13,16),(14,15),(14,16),(15,6),(16,6),(17,16)],18)
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => ([(0,1),(0,2),(1,4),(1,10),(2,3),(2,10),(3,5),(3,8),(4,5),(4,9),(5,11),(7,6),(8,7),(8,11),(9,7),(9,11),(10,8),(10,9),(11,6)],12)
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(1,13),(1,16),(1,17),(2,9),(2,13),(2,15),(2,17),(3,12),(3,14),(3,15),(3,17),(4,11),(4,14),(4,16),(4,17),(5,8),(5,11),(5,12),(5,15),(5,16),(6,8),(6,9),(6,10),(6,15),(6,16),(8,19),(8,20),(9,19),(9,22),(9,23),(10,20),(10,22),(10,23),(11,19),(11,22),(11,24),(12,20),(12,22),(12,24),(13,22),(13,23),(14,22),(14,24),(15,19),(15,20),(15,23),(15,24),(16,19),(16,20),(16,23),(16,24),(17,23),(17,24),(18,7),(19,18),(19,21),(20,18),(20,21),(21,7),(22,21),(23,18),(23,21),(24,18),(24,21)],25)
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => ([(0,2),(0,3),(0,4),(1,7),(1,8),(2,1),(2,11),(2,12),(3,9),(3,10),(3,12),(4,9),(4,10),(4,11),(5,15),(5,16),(7,15),(7,16),(8,15),(8,16),(9,5),(9,13),(10,5),(10,14),(11,7),(11,13),(11,14),(12,8),(12,13),(12,14),(13,16),(14,15),(14,16),(15,6),(16,6)],17)
[(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => ([(0,4),(0,5),(1,7),(2,9),(2,11),(3,2),(3,10),(4,3),(4,6),(5,1),(5,6),(6,7),(6,10),(7,11),(9,8),(10,9),(10,11),(11,8)],12)
[(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,18),(1,19),(2,7),(2,13),(2,15),(3,7),(3,12),(3,15),(4,8),(4,9),(4,12),(4,15),(5,8),(5,10),(5,13),(5,15),(6,1),(6,9),(6,10),(6,12),(6,13),(7,17),(8,14),(8,21),(9,14),(9,18),(9,19),(9,21),(10,14),(10,18),(10,19),(10,21),(12,17),(12,18),(12,21),(13,17),(13,19),(13,21),(14,16),(14,20),(15,17),(15,21),(16,11),(17,20),(18,16),(18,20),(19,16),(19,20),(20,11),(21,16),(21,20)],22)
[(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(1,10),(1,12),(2,8),(2,10),(2,11),(3,7),(3,8),(3,12),(4,7),(4,9),(4,11),(5,15),(5,16),(7,17),(8,13),(8,17),(9,14),(9,17),(10,13),(10,14),(11,5),(11,14),(11,17),(12,5),(12,13),(12,17),(13,15),(13,16),(14,15),(14,16),(15,6),(16,6),(17,16)],18)
[(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,7),(1,8),(2,6),(2,11),(3,6),(3,10),(4,1),(4,10),(4,11),(6,12),(7,9),(7,13),(8,9),(8,13),(9,5),(10,7),(10,12),(11,8),(11,12),(12,13),(13,5)],14)
[(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,10),(1,12),(1,29),(2,7),(2,10),(2,11),(2,29),(3,7),(3,9),(3,12),(3,29),(4,8),(4,9),(4,11),(4,29),(6,5),(7,17),(7,19),(7,27),(8,18),(8,20),(8,28),(9,17),(9,18),(9,26),(10,19),(10,20),(10,27),(10,28),(11,17),(11,20),(11,26),(11,27),(12,18),(12,19),(12,26),(12,28),(13,14),(13,15),(14,6),(14,16),(15,6),(15,16),(16,5),(17,22),(17,23),(18,22),(18,24),(19,22),(19,23),(19,25),(20,22),(20,24),(20,25),(21,16),(22,21),(23,14),(23,21),(24,15),(24,21),(25,14),(25,15),(25,21),(26,13),(26,23),(26,24),(27,13),(27,23),(27,25),(28,13),(28,24),(28,25),(29,26),(29,27),(29,28)],30)
[(1,4),(2,3),(5,6),(7,8)] => [4,3,2,1,6,5,8,7] => ([(0,4),(0,5),(0,6),(1,10),(2,3),(2,16),(2,17),(3,8),(3,9),(3,27),(4,2),(4,14),(4,15),(5,12),(5,13),(5,15),(6,12),(6,13),(6,14),(7,1),(7,24),(8,20),(8,21),(9,20),(9,21),(9,26),(10,23),(12,7),(12,18),(13,7),(13,19),(14,17),(14,18),(14,19),(15,16),(15,18),(15,19),(16,9),(16,22),(16,27),(17,8),(17,22),(17,27),(18,22),(18,24),(19,24),(19,27),(20,23),(20,25),(21,25),(22,21),(22,26),(23,11),(24,10),(24,26),(25,11),(26,23),(26,25),(27,20),(27,26)],28)
[(1,6),(2,5),(3,4),(7,8)] => [6,5,4,3,2,1,8,7] => ([(0,6),(0,7),(1,10),(2,5),(2,15),(3,12),(3,17),(4,3),(4,13),(5,4),(5,16),(6,2),(6,14),(7,1),(7,14),(8,17),(10,11),(11,8),(12,9),(13,12),(13,17),(14,10),(14,15),(15,11),(15,16),(16,8),(16,13),(17,9)],18)
[(1,8),(2,7),(3,5),(4,6)] => [8,7,5,6,3,4,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,10),(1,13),(1,26),(2,9),(2,12),(2,25),(3,11),(3,15),(3,28),(4,11),(4,16),(4,28),(5,2),(5,15),(5,17),(5,28),(6,1),(6,16),(6,17),(6,28),(8,20),(8,21),(9,18),(9,29),(10,19),(10,29),(11,24),(12,8),(12,18),(12,23),(13,8),(13,19),(13,23),(14,7),(15,9),(15,24),(15,25),(16,10),(16,24),(16,26),(17,12),(17,13),(17,25),(17,26),(18,20),(18,27),(19,21),(19,27),(20,14),(20,22),(21,14),(21,22),(22,7),(23,20),(23,21),(23,27),(24,29),(25,18),(25,23),(25,29),(26,19),(26,23),(26,29),(27,22),(28,24),(28,25),(28,26),(29,27)],30)
[(1,7),(2,8),(3,5),(4,6)] => [7,8,5,6,3,4,1,2] => ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,10),(1,12),(1,29),(2,7),(2,10),(2,11),(2,29),(3,7),(3,9),(3,12),(3,29),(4,8),(4,9),(4,11),(4,29),(6,5),(7,17),(7,19),(7,27),(8,18),(8,20),(8,28),(9,17),(9,18),(9,26),(10,19),(10,20),(10,27),(10,28),(11,17),(11,20),(11,26),(11,27),(12,18),(12,19),(12,26),(12,28),(13,14),(13,15),(14,6),(14,16),(15,6),(15,16),(16,5),(17,22),(17,23),(18,22),(18,24),(19,22),(19,23),(19,25),(20,22),(20,24),(20,25),(21,16),(22,21),(23,14),(23,21),(24,15),(24,21),(25,14),(25,15),(25,21),(26,13),(26,23),(26,24),(27,13),(27,23),(27,25),(28,13),(28,24),(28,25),(29,26),(29,27),(29,28)],30)
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => ([(0,3),(0,4),(1,6),(1,17),(2,5),(2,16),(3,2),(3,15),(4,1),(4,15),(5,7),(5,12),(6,7),(6,13),(7,18),(9,8),(10,9),(10,19),(11,9),(11,19),(12,10),(12,18),(13,11),(13,18),(14,10),(14,11),(15,16),(15,17),(16,12),(16,14),(17,13),(17,14),(18,19),(19,8)],20)
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,8,7,6,5] => ([(0,4),(0,5),(0,6),(1,10),(2,3),(2,16),(2,17),(3,8),(3,9),(3,27),(4,2),(4,14),(4,15),(5,12),(5,13),(5,15),(6,12),(6,13),(6,14),(7,1),(7,24),(8,20),(8,21),(9,20),(9,21),(9,26),(10,23),(12,7),(12,18),(13,7),(13,19),(14,17),(14,18),(14,19),(15,16),(15,18),(15,19),(16,9),(16,22),(16,27),(17,8),(17,22),(17,27),(18,22),(18,24),(19,24),(19,27),(20,23),(20,25),(21,25),(22,21),(22,26),(23,11),(24,10),(24,26),(25,11),(26,23),(26,25),(27,20),(27,26)],28)
[(1,4),(2,3),(5,8),(6,7)] => [4,3,2,1,8,7,6,5] => ([(0,3),(0,4),(1,6),(1,17),(2,5),(2,16),(3,2),(3,15),(4,1),(4,15),(5,7),(5,12),(6,7),(6,13),(7,18),(9,8),(10,9),(10,19),(11,9),(11,19),(12,10),(12,18),(13,11),(13,18),(14,10),(14,11),(15,16),(15,17),(16,12),(16,14),(17,13),(17,14),(18,19),(19,8)],20)
[(1,6),(2,7),(3,8),(4,5)] => [6,7,8,5,4,1,2,3] => ([(0,4),(0,5),(0,6),(1,14),(1,15),(2,13),(2,17),(3,12),(3,16),(4,3),(4,18),(4,20),(5,2),(5,19),(5,20),(6,1),(6,18),(6,19),(7,25),(8,26),(10,8),(10,27),(11,8),(11,28),(12,10),(12,22),(13,11),(13,23),(14,10),(14,24),(15,11),(15,24),(16,7),(16,22),(17,7),(17,23),(18,12),(18,14),(18,21),(19,13),(19,15),(19,21),(20,16),(20,17),(20,21),(21,22),(21,23),(21,24),(22,25),(22,27),(23,25),(23,28),(24,27),(24,28),(25,29),(26,9),(27,26),(27,29),(28,26),(28,29),(29,9)],30)
[(1,2),(3,8),(4,7),(5,6)] => [2,1,8,7,6,5,4,3] => ([(0,6),(0,7),(1,10),(2,5),(2,15),(3,12),(3,17),(4,3),(4,13),(5,4),(5,16),(6,2),(6,14),(7,1),(7,14),(8,17),(10,11),(11,8),(12,9),(13,12),(13,17),(14,10),(14,15),(15,11),(15,16),(16,8),(16,13),(17,9)],18)
[(1,7),(2,8),(3,6),(4,5)] => [7,8,6,5,4,3,1,2] => ([(0,4),(0,5),(0,6),(1,3),(1,12),(1,13),(2,16),(2,17),(3,2),(3,14),(3,15),(4,1),(4,10),(4,11),(5,7),(5,11),(6,7),(6,10),(7,18),(9,8),(10,12),(10,18),(11,13),(11,18),(12,14),(12,20),(13,15),(13,20),(14,16),(14,21),(15,17),(15,21),(16,9),(16,19),(17,9),(17,19),(18,20),(19,8),(20,21),(21,19)],22)
[(1,8),(2,7),(3,6),(4,5)] => [8,7,6,5,4,3,2,1] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
pattern poset
Description
The pattern poset of a permutation.
This is the poset of all non-empty permutations that occur in the given permutation as a pattern, ordered by pattern containment.