Identifier
Values
[(1,2)] => [2,1] => [1,2] => [1] => 0
[(1,2),(3,4)] => [2,1,4,3] => [3,4,1,2] => [3,1,2] => 0
[(1,3),(2,4)] => [3,4,1,2] => [2,1,4,3] => [2,1,3] => 0
[(1,4),(2,3)] => [3,4,2,1] => [1,2,4,3] => [1,2,3] => 1
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => [5,3,4,1,2] => 0
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [5,6,2,1,4,3] => [5,2,1,4,3] => 0
[(1,4),(2,3),(5,6)] => [3,4,2,1,6,5] => [5,6,1,2,4,3] => [5,1,2,4,3] => 1
[(1,5),(2,3),(4,6)] => [3,5,2,6,1,4] => [4,1,6,2,5,3] => [4,1,2,5,3] => 1
[(1,6),(2,3),(4,5)] => [3,5,2,6,4,1] => [1,4,6,2,5,3] => [1,4,2,5,3] => 1
[(1,6),(2,4),(3,5)] => [4,5,6,2,3,1] => [1,3,2,6,5,4] => [1,3,2,5,4] => 1
[(1,5),(2,4),(3,6)] => [4,5,6,2,1,3] => [3,1,2,6,5,4] => [3,1,2,5,4] => 1
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [3,2,1,5,4] => 0
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [4,2,6,1,5,3] => [4,2,1,5,3] => 0
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [4,3,6,5,1,2] => [4,3,5,1,2] => 0
[(1,2),(3,6),(4,5)] => [2,1,5,6,4,3] => [3,4,6,5,1,2] => [3,4,5,1,2] => 1
[(1,3),(2,6),(4,5)] => [3,5,1,6,4,2] => [2,4,6,1,5,3] => [2,4,1,5,3] => 1
[(1,4),(2,6),(3,5)] => [4,5,6,1,3,2] => [2,3,1,6,5,4] => [2,3,1,5,4] => 1
[(1,5),(2,6),(3,4)] => [4,5,6,3,1,2] => [2,1,3,6,5,4] => [2,1,3,5,4] => 2
[(1,6),(2,5),(3,4)] => [4,5,6,3,2,1] => [1,2,3,6,5,4] => [1,2,3,5,4] => 2
[(1,8),(2,7),(3,4),(5,6)] => [4,6,7,3,8,5,2,1] => [1,2,5,8,3,7,6,4] => [1,2,5,3,7,6,4] => 2
[(1,8),(2,7),(3,5),(4,6)] => [5,6,7,8,3,4,2,1] => [1,2,4,3,8,7,6,5] => [1,2,4,3,7,6,5] => 2
[(1,8),(2,6),(3,5),(4,7)] => [5,6,7,8,3,2,4,1] => [1,4,2,3,8,7,6,5] => [1,4,2,3,7,6,5] => 2
[(1,8),(2,5),(3,6),(4,7)] => [5,6,7,8,2,3,4,1] => [1,4,3,2,8,7,6,5] => [1,4,3,2,7,6,5] => 1
[(1,8),(2,3),(4,7),(5,6)] => [3,6,2,7,8,5,4,1] => [1,4,5,8,7,2,6,3] => [1,4,5,7,2,6,3] => 2
[(1,8),(2,4),(3,7),(5,6)] => [4,6,7,2,8,5,3,1] => [1,3,5,8,2,7,6,4] => [1,3,5,2,7,6,4] => 2
[(1,8),(2,5),(3,7),(4,6)] => [5,6,7,8,2,4,3,1] => [1,3,4,2,8,7,6,5] => [1,3,4,2,7,6,5] => 2
[(1,8),(2,6),(3,7),(4,5)] => [5,6,7,8,4,2,3,1] => [1,3,2,4,8,7,6,5] => [1,3,2,4,7,6,5] => 3
[(1,8),(2,7),(3,6),(4,5)] => [5,6,7,8,4,3,2,1] => [1,2,3,4,8,7,6,5] => [1,2,3,4,7,6,5] => 3
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Description
The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation.
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
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
Map
restriction
Description
The permutation obtained by removing the largest letter.
This map is undefined for the empty permutation.