Identifier
Values
[1,0] => [1] => [1] => 0
[1,0,1,0] => [2,1] => [2,1] => 1
[1,1,0,0] => [1,2] => [1,2] => 0
[1,0,1,0,1,0] => [2,1,3] => [2,1,3] => 1
[1,0,1,1,0,0] => [2,3,1] => [2,3,1] => 1
[1,1,0,0,1,0] => [3,1,2] => [3,1,2] => 1
[1,1,0,1,0,0] => [1,3,2] => [1,3,2] => 1
[1,1,1,0,0,0] => [1,2,3] => [1,2,3] => 0
[1,0,1,0,1,0,1,0] => [2,1,4,3] => [2,1,4,3] => 2
[1,0,1,0,1,1,0,0] => [2,4,1,3] => [2,4,1,3] => 2
[1,0,1,1,0,0,1,0] => [2,1,3,4] => [2,1,3,4] => 1
[1,0,1,1,0,1,0,0] => [2,3,1,4] => [2,3,1,4] => 1
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [2,3,4,1] => 1
[1,1,0,0,1,0,1,0] => [3,1,4,2] => [3,1,4,2] => 1
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [3,4,1,2] => 1
[1,1,0,1,0,0,1,0] => [3,1,2,4] => [3,1,2,4] => 1
[1,1,0,1,0,1,0,0] => [1,3,2,4] => [1,3,2,4] => 1
[1,1,0,1,1,0,0,0] => [1,3,4,2] => [1,3,4,2] => 1
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [4,1,2,3] => 1
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [1,4,2,3] => 1
[1,1,1,0,1,0,0,0] => [1,2,4,3] => [1,2,4,3] => 1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => 0
[1,1,0,1,0,1,0,1,0,0] => [1,3,2,5,4] => [1,3,2,5,4] => 2
[1,1,0,1,0,1,1,0,0,0] => [1,3,5,2,4] => [1,3,5,2,4] => 2
[1,1,0,1,1,0,0,1,0,0] => [1,3,2,4,5] => [1,3,2,4,5] => 1
[1,1,0,1,1,0,1,0,0,0] => [1,3,4,2,5] => [1,3,4,2,5] => 1
[1,1,0,1,1,1,0,0,0,0] => [1,3,4,5,2] => [1,3,4,5,2] => 1
[1,1,1,0,0,1,0,1,0,0] => [1,4,2,5,3] => [1,4,2,5,3] => 1
[1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => [1,4,5,2,3] => 1
[1,1,1,0,1,0,0,1,0,0] => [1,4,2,3,5] => [1,4,2,3,5] => 1
[1,1,1,0,1,0,1,0,0,0] => [1,2,4,3,5] => [1,2,4,3,5] => 1
[1,1,1,0,1,1,0,0,0,0] => [1,2,4,5,3] => [1,2,4,5,3] => 1
[1,1,1,1,0,0,0,1,0,0] => [1,5,2,3,4] => [1,5,2,3,4] => 1
[1,1,1,1,0,0,1,0,0,0] => [1,2,5,3,4] => [1,2,5,3,4] => 1
[1,1,1,1,0,1,0,0,0,0] => [1,2,3,5,4] => [1,2,3,5,4] => 1
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => 0
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Description
The number of right descents of a signed permutations.
An index is a right descent if it is a left descent of the inverse signed permutation.
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
to signed permutation
Description
The signed permutation with all signs positive.