Identifier
Values
[(1,2)] => [2,1] => [1,2] => [1,2] => 0
[(1,2),(3,4)] => [2,1,4,3] => [1,2,3,4] => [1,2,3,4] => 0
[(1,3),(2,4)] => [3,4,1,2] => [1,3,2,4] => [3,1,2,4] => 0
[(1,4),(2,3)] => [3,4,2,1] => [1,3,2,4] => [3,1,2,4] => 0
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => 0
[(1,4),(2,3),(5,6)] => [3,4,2,1,6,5] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => 0
[(1,5),(2,3),(4,6)] => [3,5,2,6,1,4] => [1,3,2,5,4,6] => [3,5,1,2,4,6] => 1
[(1,6),(2,3),(4,5)] => [3,5,2,6,4,1] => [1,3,2,5,4,6] => [3,5,1,2,4,6] => 1
[(1,6),(2,4),(3,5)] => [4,5,6,2,3,1] => [1,4,2,5,3,6] => [1,4,5,2,3,6] => 1
[(1,5),(2,4),(3,6)] => [4,5,6,2,1,3] => [1,4,2,5,3,6] => [1,4,5,2,3,6] => 1
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [1,4,2,5,3,6] => [1,4,5,2,3,6] => 1
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [1,3,2,5,4,6] => [3,5,1,2,4,6] => 1
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => 0
[(1,2),(3,6),(4,5)] => [2,1,5,6,4,3] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => 0
[(1,3),(2,6),(4,5)] => [3,5,1,6,4,2] => [1,3,2,5,4,6] => [3,5,1,2,4,6] => 1
[(1,4),(2,6),(3,5)] => [4,5,6,1,3,2] => [1,4,2,5,3,6] => [1,4,5,2,3,6] => 1
[(1,5),(2,6),(3,4)] => [4,5,6,3,1,2] => [1,4,3,6,2,5] => [4,6,3,1,2,5] => 1
[(1,6),(2,5),(3,4)] => [4,5,6,3,2,1] => [1,4,3,6,2,5] => [4,6,3,1,2,5] => 1
[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => 0
[(1,2),(3,6),(4,5),(7,8)] => [2,1,5,6,4,3,8,7] => [1,2,3,5,4,6,7,8] => [5,1,2,3,4,6,7,8] => 0
[(1,2),(3,7),(4,5),(6,8)] => [2,1,5,7,4,8,3,6] => [1,2,3,5,4,7,6,8] => [5,7,1,2,3,4,6,8] => 1
[(1,2),(3,8),(4,5),(6,7)] => [2,1,5,7,4,8,6,3] => [1,2,3,5,4,7,6,8] => [5,7,1,2,3,4,6,8] => 1
[(1,2),(3,8),(4,6),(5,7)] => [2,1,6,7,8,4,5,3] => [1,2,3,6,4,7,5,8] => [1,6,7,2,3,4,5,8] => 1
[(1,2),(3,7),(4,6),(5,8)] => [2,1,6,7,8,4,3,5] => [1,2,3,6,4,7,5,8] => [1,6,7,2,3,4,5,8] => 1
[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [1,2,3,6,4,7,5,8] => [1,6,7,2,3,4,5,8] => 1
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [1,2,3,5,4,7,6,8] => [5,7,1,2,3,4,6,8] => 1
[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => 0
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,7,8,6,5] => [1,2,3,4,5,7,6,8] => [7,1,2,3,4,5,6,8] => 0
[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,7,3,8,6,4] => [1,2,3,5,4,7,6,8] => [5,7,1,2,3,4,6,8] => 1
[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,7,8,3,5,4] => [1,2,3,6,4,7,5,8] => [1,6,7,2,3,4,5,8] => 1
[(1,2),(3,4),(5,6),(7,8),(9,10)] => [2,1,4,3,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[(1,2),(3,4),(5,6),(7,9),(8,10)] => [2,1,4,3,6,5,9,10,7,8] => [1,2,3,4,5,6,7,9,8,10] => [9,1,2,3,4,5,6,7,8,10] => 0
[(1,2),(3,4),(5,6),(7,10),(8,9)] => [2,1,4,3,6,5,9,10,8,7] => [1,2,3,4,5,6,7,9,8,10] => [9,1,2,3,4,5,6,7,8,10] => 0
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The number of boxed occurrences of 132 in a permutation.
This is the number of occurrences of the pattern $132$ such that any entry between the three matched entries is either larger than the largest matched entry or smaller than the smallest matched entry.
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
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.