Identifier
Values
[(1,2)] => [2,1] => [1] => [1] => 0
[(1,2),(3,4)] => [2,1,4,3] => [2,1,3] => [2,1,3] => 0
[(1,3),(2,4)] => [3,4,1,2] => [3,1,2] => [1,3,2] => 0
[(1,4),(2,3)] => [4,3,2,1] => [3,2,1] => [3,2,1] => 0
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [2,1,4,3,5] => [3,2,4,1,5] => 1
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [3,4,1,2,5] => [1,4,2,3,5] => 1
[(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => [4,3,2,1,5] => [4,3,2,1,5] => 1
[(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => [5,3,2,1,4] => [4,3,1,5,2] => 1
[(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => [3,2,5,4,1] => [5,3,2,4,1] => 0
[(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => [4,5,2,3,1] => [5,1,4,2,3] => 1
[(1,5),(2,4),(3,6)] => [5,4,6,2,1,3] => [5,4,2,1,3] => [4,1,5,3,2] => 1
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [4,5,1,2,3] => [1,2,5,3,4] => 1
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [3,5,1,2,4] => [1,2,4,5,3] => 0
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [2,1,5,3,4] => [3,2,1,5,4] => 1
[(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => [2,1,5,4,3] => [4,3,5,2,1] => 0
[(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => [3,1,5,4,2] => [4,5,2,3,1] => 0
[(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => [4,5,1,3,2] => [2,5,4,1,3] => 1
[(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => [5,4,3,1,2] => [1,5,4,3,2] => 1
[(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[(1,4),(2,3),(5,6),(7,8)] => [4,3,2,1,6,5,8,7] => [4,3,2,1,6,5,7] => [5,4,3,2,6,1,7] => 2
[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [4,5,6,1,2,3,7] => [1,2,6,3,4,5,7] => 1
[(1,2),(3,6),(4,5),(7,8)] => [2,1,6,5,4,3,8,7] => [2,1,6,5,4,3,7] => [5,4,6,3,2,1,7] => 1
[(1,6),(2,5),(3,4),(7,8)] => [6,5,4,3,2,1,8,7] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 1
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [5,6,7,1,2,3,4] => [1,2,3,7,4,5,6] => 1
[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [4,6,7,1,2,3,5] => [1,2,3,5,7,4,6] => 0
[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => [4,5,7,1,2,3,6] => [1,2,3,5,6,7,4] => 0
[(1,4),(2,3),(5,7),(6,8)] => [4,3,2,1,7,8,5,6] => [4,3,2,1,7,5,6] => [5,4,3,2,1,7,6] => 1
[(1,7),(2,5),(3,8),(4,6)] => [7,5,8,6,2,4,1,3] => [7,5,6,2,4,1,3] => [1,3,7,6,2,5,4] => 2
[(1,6),(2,7),(3,8),(4,5)] => [6,7,8,5,4,1,2,3] => [6,7,5,4,1,2,3] => [1,2,7,6,5,3,4] => 1
[(1,7),(2,8),(3,6),(4,5)] => [7,8,6,5,4,3,1,2] => [7,6,5,4,3,1,2] => [1,7,6,5,4,3,2] => 1
[(1,8),(2,7),(3,6),(4,5)] => [8,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
[(1,2),(3,8),(4,7),(5,6),(9,10)] => [2,1,8,7,6,5,4,3,10,9] => [2,1,8,7,6,5,4,3,9] => [7,6,8,5,4,3,2,1,9] => 1
[(1,8),(2,7),(3,6),(4,5),(9,10)] => [8,7,6,5,4,3,2,1,10,9] => [8,7,6,5,4,3,2,1,9] => [8,7,6,5,4,3,2,1,9] => 1
[(1,10),(2,9),(3,8),(4,7),(5,6)] => [10,9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 0
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [10,9,8,7,6,5,4,3,2,1,12,11] => [10,9,8,7,6,5,4,3,2,1,11] => [10,9,8,7,6,5,4,3,2,1,11] => 1
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 very big ascents of a permutation.
A very big ascent of a permutation $\pi$ is an index $i$ such that $\pi_{i+1} - \pi_i > 2$.
For the number of ascents, see St000245The number of ascents of a permutation. and for the number of big ascents, see St000646The number of big ascents of a permutation.. General $r$-ascents were for example be studied in [1, Section 2].
Map
restriction
Description
The permutation obtained by removing the largest letter.
This map is undefined for the empty permutation.
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.