Identifier
Values
[1] => [1,0] => [1,0] => [2,1] => 0
[1,1] => [1,0,1,0] => [1,1,0,0] => [2,3,1] => 0
[2] => [1,1,0,0] => [1,0,1,0] => [3,1,2] => 0
[1,1,1] => [1,0,1,0,1,0] => [1,1,0,0,1,0] => [2,4,1,3] => 0
[1,2] => [1,0,1,1,0,0] => [1,1,0,1,0,0] => [4,3,1,2] => 0
[2,1] => [1,1,0,0,1,0] => [1,1,1,0,0,0] => [2,3,4,1] => 0
[3] => [1,1,1,0,0,0] => [1,0,1,0,1,0] => [4,1,2,3] => 0
[1,1,1,1] => [1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0] => [2,4,1,5,3] => 0
[1,1,2] => [1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => [4,3,1,5,2] => 0
[1,2,1] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,0] => [2,5,1,3,4] => 0
[1,3] => [1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,0] => [5,4,1,2,3] => 0
[2,1,1] => [1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,0] => [2,5,4,1,3] => 0
[2,2] => [1,1,0,0,1,1,0,0] => [1,1,1,1,0,0,0,0] => [2,3,4,5,1] => 0
[3,1] => [1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0] => [5,3,4,1,2] => 0
[4] => [1,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,0] => [5,1,2,3,4] => 0
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => 0
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => 0
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => 0
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => 0
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => 0
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => 0
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => 0
[1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => 0
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => 0
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => 1
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => 0
[2,3] => [1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => 0
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => 0
[3,2] => [1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => 0
[4,1] => [1,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => 0
[5] => [1,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => 0
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searching the database for the individual values of this statistic
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Description
The number of right ropes of a permutation.
Let $\pi$ be a permutation of length $n$. A raft of $\pi$ is a non-empty maximal sequence of consecutive small ascents, St000441The number of successions of a permutation., and a right rope is a large ascent after a raft of $\pi$.
See Definition 3.10 and Example 3.11 in [1].
Map
Elizalde-Deutsch bijection
Description
The Elizalde-Deutsch bijection on Dyck paths.
.Let $n$ be the length of the Dyck path. Consider the steps $1,n,2,n-1,\dots$ of $D$. When considering the $i$-th step its corresponding matching step has not yet been read, let the $i$-th step of the image of $D$ be an up step, otherwise let it be a down step.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
bounce path
Description
The bounce path determined by an integer composition.