Identifier
Mp00283: Perfect matchings —non-nesting-exceedence 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)] => [3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[(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)] => [3,4,2,1,6,5] => ([(0,3),(0,4),(0,5),(1,6),(1,9),(2,7),(2,8),(3,1),(3,11),(3,13),(4,2),(4,12),(4,13),(5,11),(5,12),(6,15),(7,16),(8,15),(8,16),(9,15),(9,16),(11,9),(11,14),(12,7),(12,14),(13,6),(13,8),(13,14),(14,15),(14,16),(15,10),(16,10)],17)
[(1,5),(2,3),(4,6)] => [3,5,2,6,1,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,9),(1,18),(1,22),(2,11),(2,14),(2,16),(2,18),(3,9),(3,14),(3,15),(3,22),(4,12),(4,13),(4,16),(4,22),(5,10),(5,13),(5,15),(5,18),(5,22),(6,8),(6,10),(6,11),(6,12),(6,22),(8,20),(8,25),(9,19),(9,25),(10,20),(10,21),(10,25),(10,26),(11,17),(11,25),(11,26),(12,17),(12,20),(12,26),(13,21),(13,26),(14,19),(14,26),(15,19),(15,21),(15,25),(16,17),(16,26),(17,24),(18,19),(18,25),(18,26),(19,23),(20,23),(20,24),(21,23),(21,24),(22,20),(22,21),(22,25),(22,26),(23,7),(24,7),(25,23),(25,24),(26,23),(26,24)],27)
[(1,6),(2,3),(4,5)] => [3,5,2,6,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,18),(1,19),(2,10),(2,13),(2,19),(2,20),(3,9),(3,13),(3,18),(3,20),(4,12),(4,14),(4,18),(4,19),(4,20),(5,11),(5,14),(5,18),(5,19),(5,20),(6,8),(6,9),(6,10),(6,11),(6,12),(8,21),(8,22),(9,15),(9,21),(9,25),(10,15),(10,22),(10,25),(11,16),(11,21),(11,22),(11,25),(12,16),(12,21),(12,22),(12,25),(13,15),(13,25),(14,16),(14,17),(14,25),(15,24),(16,23),(16,24),(17,23),(18,17),(18,21),(18,25),(19,17),(19,22),(19,25),(20,17),(20,25),(21,23),(21,24),(22,23),(22,24),(23,7),(24,7),(25,23),(25,24)],26)
[(1,6),(2,4),(3,5)] => [4,5,6,2,3,1] => ([(0,3),(0,4),(0,5),(1,13),(2,6),(2,7),(2,14),(3,9),(3,10),(4,9),(4,11),(5,2),(5,10),(5,11),(6,12),(7,12),(7,13),(9,1),(9,14),(10,6),(10,14),(11,7),(11,14),(12,8),(13,8),(14,12),(14,13)],15)
[(1,5),(2,4),(3,6)] => [4,5,6,2,1,3] => ([(0,3),(0,4),(0,6),(1,14),(2,14),(2,15),(3,8),(3,12),(4,9),(4,12),(5,2),(5,10),(5,11),(6,5),(6,8),(6,9),(8,11),(8,13),(9,10),(9,13),(10,15),(11,14),(11,15),(12,1),(12,13),(13,14),(13,15),(14,7),(15,7)],16)
[(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)] => [2,1,5,6,4,3] => ([(0,3),(0,4),(0,5),(1,6),(1,9),(2,7),(2,8),(3,1),(3,11),(3,13),(4,2),(4,12),(4,13),(5,11),(5,12),(6,15),(7,16),(8,15),(8,16),(9,15),(9,16),(11,9),(11,14),(12,7),(12,14),(13,6),(13,8),(13,14),(14,15),(14,16),(15,10),(16,10)],17)
[(1,3),(2,6),(4,5)] => [3,5,1,6,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(1,9),(1,18),(1,22),(2,11),(2,14),(2,16),(2,18),(3,9),(3,14),(3,15),(3,22),(4,12),(4,13),(4,16),(4,22),(5,10),(5,13),(5,15),(5,18),(5,22),(6,8),(6,10),(6,11),(6,12),(6,22),(8,20),(8,25),(9,19),(9,25),(10,20),(10,21),(10,25),(10,26),(11,17),(11,25),(11,26),(12,17),(12,20),(12,26),(13,21),(13,26),(14,19),(14,26),(15,19),(15,21),(15,25),(16,17),(16,26),(17,24),(18,19),(18,25),(18,26),(19,23),(20,23),(20,24),(21,23),(21,24),(22,20),(22,21),(22,25),(22,26),(23,7),(24,7),(25,23),(25,24),(26,23),(26,24)],27)
[(1,4),(2,6),(3,5)] => [4,5,6,1,3,2] => ([(0,3),(0,4),(0,6),(1,14),(2,14),(2,15),(3,8),(3,12),(4,9),(4,12),(5,2),(5,10),(5,11),(6,5),(6,8),(6,9),(8,11),(8,13),(9,10),(9,13),(10,15),(11,14),(11,15),(12,1),(12,13),(13,14),(13,15),(14,7),(15,7)],16)
[(1,5),(2,6),(3,4)] => [4,5,6,3,1,2] => ([(0,3),(0,4),(0,5),(1,14),(2,6),(2,7),(3,9),(3,10),(4,9),(4,11),(5,2),(5,10),(5,11),(6,13),(7,13),(7,14),(9,1),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(12,14),(13,8),(14,8)],15)
[(1,6),(2,5),(3,4)] => [4,5,6,3,2,1] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
[(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)
[(1,8),(2,7),(3,5),(4,6)] => [5,6,7,8,3,4,2,1] => ([(0,5),(0,6),(0,7),(1,10),(2,12),(2,17),(3,4),(3,18),(3,20),(4,9),(4,16),(4,27),(5,14),(5,15),(6,2),(6,15),(6,19),(7,3),(7,14),(7,19),(8,23),(8,25),(9,22),(10,23),(12,1),(12,24),(13,8),(13,26),(14,18),(14,21),(15,12),(15,21),(16,8),(16,22),(16,26),(17,13),(17,24),(18,9),(18,27),(19,17),(19,20),(19,21),(20,13),(20,16),(20,27),(21,24),(21,27),(22,25),(23,11),(24,10),(24,26),(25,11),(26,23),(26,25),(27,22),(27,26)],28)
[(1,7),(2,8),(3,5),(4,6)] => [5,6,7,8,3,4,1,2] => ([(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)
[(1,7),(2,6),(3,5),(4,8)] => [5,6,7,8,3,2,1,4] => ([(0,6),(0,7),(0,8),(1,10),(2,12),(2,27),(3,14),(3,18),(4,5),(4,19),(4,22),(5,2),(5,9),(5,21),(6,15),(6,16),(7,3),(7,16),(7,20),(8,4),(8,15),(8,20),(9,27),(10,28),(11,28),(11,29),(12,28),(12,29),(14,1),(14,26),(15,19),(15,23),(16,14),(16,23),(17,11),(17,24),(18,17),(18,26),(19,9),(19,25),(20,18),(20,22),(20,23),(21,11),(21,12),(21,27),(22,17),(22,21),(22,25),(23,25),(23,26),(24,28),(24,29),(25,24),(25,27),(26,10),(26,24),(27,29),(28,13),(29,13)],30)
[(1,8),(2,5),(3,6),(4,7)] => [5,6,7,8,2,3,4,1] => ([(0,5),(0,6),(0,7),(1,20),(2,11),(2,16),(3,4),(3,17),(3,19),(4,9),(4,15),(4,26),(5,12),(5,13),(6,2),(6,13),(6,18),(7,3),(7,12),(7,18),(8,22),(9,20),(9,24),(11,1),(11,26),(12,17),(12,21),(13,11),(13,21),(14,8),(14,27),(15,8),(15,24),(15,27),(16,14),(16,26),(17,9),(17,23),(18,16),(18,19),(18,21),(19,14),(19,15),(19,23),(20,25),(21,23),(21,26),(22,10),(23,24),(23,27),(24,22),(24,25),(25,10),(26,20),(26,27),(27,22),(27,25)],28)
[(1,6),(2,5),(3,7),(4,8)] => [5,6,7,8,2,1,3,4] => ([(0,6),(0,7),(0,8),(1,27),(2,10),(2,27),(3,13),(3,17),(4,5),(4,18),(4,21),(5,2),(5,12),(5,20),(6,15),(6,16),(7,3),(7,16),(7,19),(8,4),(8,15),(8,19),(9,28),(10,28),(10,29),(12,24),(12,27),(13,1),(13,23),(14,9),(14,26),(15,18),(15,22),(16,13),(16,22),(17,14),(17,23),(18,12),(18,25),(19,17),(19,21),(19,22),(20,9),(20,10),(20,24),(21,14),(21,20),(21,25),(22,23),(22,25),(23,26),(23,27),(24,28),(24,29),(25,24),(25,26),(26,28),(26,29),(27,29),(28,11),(29,11)],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)
[(1,5),(2,6),(3,8),(4,7)] => [5,6,7,8,1,2,4,3] => ([(0,6),(0,7),(0,8),(1,27),(2,10),(2,27),(3,13),(3,17),(4,5),(4,18),(4,21),(5,2),(5,12),(5,20),(6,15),(6,16),(7,3),(7,16),(7,19),(8,4),(8,15),(8,19),(9,28),(10,28),(10,29),(12,24),(12,27),(13,1),(13,23),(14,9),(14,26),(15,18),(15,22),(16,13),(16,22),(17,14),(17,23),(18,12),(18,25),(19,17),(19,21),(19,22),(20,9),(20,10),(20,24),(21,14),(21,20),(21,25),(22,23),(22,25),(23,26),(23,27),(24,28),(24,29),(25,24),(25,26),(26,28),(26,29),(27,29),(28,11),(29,11)],30)
[(1,6),(2,7),(3,8),(4,5)] => [5,6,7,8,4,1,2,3] => ([(0,5),(0,6),(0,7),(1,22),(2,11),(2,17),(3,4),(3,16),(3,19),(4,9),(4,15),(5,12),(5,13),(6,2),(6,13),(6,18),(7,3),(7,12),(7,18),(8,26),(9,21),(9,22),(11,1),(11,24),(12,16),(12,20),(13,11),(13,20),(14,8),(14,25),(15,8),(15,21),(16,9),(16,23),(17,14),(17,24),(18,17),(18,19),(18,20),(19,14),(19,15),(19,23),(20,23),(20,24),(21,26),(21,27),(22,27),(23,21),(23,25),(24,22),(24,25),(25,26),(25,27),(26,10),(27,10)],28)
[(1,5),(2,8),(3,7),(4,6)] => [5,6,7,8,1,4,3,2] => ([(0,6),(0,7),(0,8),(1,10),(2,12),(2,27),(3,14),(3,18),(4,5),(4,19),(4,22),(5,2),(5,9),(5,21),(6,15),(6,16),(7,3),(7,16),(7,20),(8,4),(8,15),(8,20),(9,27),(10,28),(11,28),(11,29),(12,28),(12,29),(14,1),(14,26),(15,19),(15,23),(16,14),(16,23),(17,11),(17,24),(18,17),(18,26),(19,9),(19,25),(20,18),(20,22),(20,23),(21,11),(21,12),(21,27),(22,17),(22,21),(22,25),(23,25),(23,26),(24,28),(24,29),(25,24),(25,27),(26,10),(26,24),(27,29),(28,13),(29,13)],30)
[(1,7),(2,8),(3,6),(4,5)] => [5,6,7,8,4,3,1,2] => ([(0,5),(0,6),(0,7),(1,10),(2,12),(2,17),(3,4),(3,18),(3,20),(4,9),(4,16),(5,13),(5,14),(6,2),(6,14),(6,19),(7,3),(7,13),(7,19),(8,24),(8,26),(9,23),(10,24),(12,1),(12,22),(13,18),(13,21),(14,12),(14,21),(15,8),(15,27),(16,8),(16,23),(17,15),(17,22),(18,9),(18,25),(19,17),(19,20),(19,21),(20,15),(20,16),(20,25),(21,22),(21,25),(22,10),(22,27),(23,26),(24,11),(25,23),(25,27),(26,11),(27,24),(27,26)],28)
[(1,8),(2,7),(3,6),(4,5)] => [5,6,7,8,4,3,2,1] => ([(0,6),(0,7),(1,4),(1,16),(2,5),(2,15),(3,13),(4,12),(5,3),(5,19),(6,1),(6,17),(7,2),(7,17),(9,11),(10,8),(11,8),(12,9),(13,10),(14,9),(14,18),(15,14),(15,19),(16,12),(16,14),(17,15),(17,16),(18,10),(18,11),(19,13),(19,18)],20)
Map
non-nesting-exceedence permutation
Description
The fixed-point-free permutation with deficiencies given by the perfect matching, no alignments and no inversions between exceedences.
Put differently, the exceedences form the unique non-nesting perfect matching whose openers coincide with those of the given 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.