Identifier
-
Mp00132:
Dyck paths
—switch returns and last double rise⟶
Dyck paths
St001186: Dyck paths ⟶ ℤ
Values
[1,0] => [1,0] => 0
[1,0,1,0] => [1,0,1,0] => 0
[1,1,0,0] => [1,1,0,0] => 0
[1,0,1,0,1,0] => [1,0,1,0,1,0] => 1
[1,0,1,1,0,0] => [1,1,0,1,0,0] => 0
[1,1,0,0,1,0] => [1,1,0,0,1,0] => 0
[1,1,0,1,0,0] => [1,0,1,1,0,0] => 0
[1,1,1,0,0,0] => [1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,0] => 0
[1,1,0,0,1,0,1,0] => [1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,0] => 1
[1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,0] => [1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0] => [1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,0] => [1,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0] => [1,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,0,1,1,1,0,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,0,1,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 0
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Description
Number of simple modules with grade at least 3 in the corresponding Nakayama algebra.
Map
switch returns and last double rise
Description
An alternative to the Adin-Bagno-Roichman transformation of a Dyck path.
This is a bijection preserving the number of up steps before each peak and exchanging the number of components with the position of the last double rise.
This is a bijection preserving the number of up steps before each peak and exchanging the number of components with the position of the last double rise.
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