Identifier
Values
[[1]] => [(1,2)] => [2,1] => [1,2] => 1
[[1,0],[0,1]] => [(1,4),(2,3)] => [4,3,2,1] => [1,2,3,4] => 3
[[0,1],[1,0]] => [(1,2),(3,4)] => [2,1,4,3] => [1,4,2,3] => 2
[[1,0,0],[0,1,0],[0,0,1]] => [(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => 5
[[0,1,0],[1,0,0],[0,0,1]] => [(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [1,4,2,3,6,5] => 3
[[1,0,0],[0,0,1],[0,1,0]] => [(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => [1,2,5,3,4,6] => 4
[[0,1,0],[1,-1,1],[0,1,0]] => [(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => [1,6,2,3,4,5] => 4
[[0,0,1],[1,0,0],[0,1,0]] => [(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => [1,2,5,3,4,6] => 4
[[0,1,0],[0,0,1],[1,0,0]] => [(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [1,4,2,3,6,5] => 3
[[0,0,1],[0,1,0],[1,0,0]] => [(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => [1,6,2,3,4,5] => 4
[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]] => [(1,8),(2,7),(3,6),(4,5)] => [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => 7
[[0,1,0,0],[1,-1,1,0],[0,1,0,0],[0,0,0,1]] => [(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => [1,8,2,3,4,7,5,6] => 5
[[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]] => [(1,6),(2,3),(4,5),(7,8)] => [6,3,2,5,4,1,8,7] => [1,8,2,5,3,4,6,7] => 5
[[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]] => [(1,8),(2,7),(3,4),(5,6)] => [8,7,4,3,6,5,2,1] => [1,2,3,6,4,5,7,8] => 6
[[0,1,0,0],[1,-1,1,0],[0,1,-1,1],[0,0,1,0]] => [(1,2),(3,8),(4,7),(5,6)] => [2,1,8,7,6,5,4,3] => [1,8,2,3,4,5,6,7] => 6
[[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]] => [(1,8),(2,7),(3,4),(5,6)] => [8,7,4,3,6,5,2,1] => [1,2,3,6,4,5,7,8] => 6
[[0,0,1,0],[1,0,-1,1],[0,1,0,0],[0,0,1,0]] => [(1,8),(2,7),(3,4),(5,6)] => [8,7,4,3,6,5,2,1] => [1,2,3,6,4,5,7,8] => 6
[[0,1,0,0],[1,-1,1,0],[0,0,0,1],[0,1,0,0]] => [(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => [1,8,2,3,4,7,5,6] => 5
[[0,0,1,0],[0,1,0,0],[1,-1,0,1],[0,1,0,0]] => [(1,6),(2,3),(4,5),(7,8)] => [6,3,2,5,4,1,8,7] => [1,8,2,5,3,4,6,7] => 5
[[0,0,1,0],[0,1,-1,1],[1,-1,1,0],[0,1,0,0]] => [(1,6),(2,5),(3,4),(7,8)] => [6,5,4,3,2,1,8,7] => [1,8,2,3,4,5,6,7] => 6
[[0,0,0,1],[0,1,0,0],[1,-1,1,0],[0,1,0,0]] => [(1,6),(2,3),(4,5),(7,8)] => [6,3,2,5,4,1,8,7] => [1,8,2,5,3,4,6,7] => 5
[[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,0]] => [(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => [1,8,2,3,4,7,5,6] => 5
[[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]] => [(1,4),(2,3),(5,8),(6,7)] => [4,3,2,1,8,7,6,5] => [1,8,2,3,4,5,6,7] => 6
[[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => [10,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => 9
[[0,1,0,0,0],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[0,0,0,1,0]] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => [2,1,10,9,8,7,6,5,4,3] => [1,10,2,3,4,5,6,7,8,9] => 8
[[0,0,1,0,0],[0,1,-1,1,0],[1,-1,1,-1,1],[0,1,-1,1,0],[0,0,1,0,0]] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => [8,7,6,5,4,3,2,1,10,9] => [1,10,2,3,4,5,6,7,8,9] => 8
[[0,0,0,1,0],[0,0,1,-1,1],[0,1,-1,1,0],[1,-1,1,0,0],[0,1,0,0,0]] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => [4,3,2,1,10,9,8,7,6,5] => [1,10,2,3,4,5,6,7,8,9] => 8
[[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0]] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => [6,5,4,3,2,1,10,9,8,7] => [1,10,2,3,4,5,6,7,8,9] => 8
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Description
The number of ascents of a permutation.
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
Map
link pattern
Description
Sends an alternating sign matrix to the link pattern of the corresponding fully packed loop configuration.
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.