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Matching statistic: St001232
Mp00256: Decorated permutations —upper permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00032: Dyck paths —inverse zeta map⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00032: Dyck paths —inverse zeta map⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[+] => [1] => [1,0]
=> [1,0]
=> 0
[-] => [1] => [1,0]
=> [1,0]
=> 0
[+,+] => [1,2] => [1,0,1,0]
=> [1,1,0,0]
=> 0
[-,+] => [2,1] => [1,1,0,0]
=> [1,0,1,0]
=> 1
[+,-] => [1,2] => [1,0,1,0]
=> [1,1,0,0]
=> 0
[-,-] => [1,2] => [1,0,1,0]
=> [1,1,0,0]
=> 0
[2,1] => [2,1] => [1,1,0,0]
=> [1,0,1,0]
=> 1
[+,+,+] => [1,2,3] => [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 0
[-,+,+] => [2,3,1] => [1,1,0,1,0,0]
=> [1,1,0,0,1,0]
=> 1
[+,-,+] => [1,3,2] => [1,0,1,1,0,0]
=> [1,0,1,1,0,0]
=> 2
[+,+,-] => [1,2,3] => [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 0
[-,+,-] => [2,1,3] => [1,1,0,0,1,0]
=> [1,1,0,1,0,0]
=> 2
[+,-,-] => [1,2,3] => [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 0
[-,-,-] => [1,2,3] => [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 0
[+,3,2] => [1,3,2] => [1,0,1,1,0,0]
=> [1,0,1,1,0,0]
=> 2
[2,1,+] => [2,3,1] => [1,1,0,1,0,0]
=> [1,1,0,0,1,0]
=> 1
[2,1,-] => [2,1,3] => [1,1,0,0,1,0]
=> [1,1,0,1,0,0]
=> 2
[3,1,2] => [2,3,1] => [1,1,0,1,0,0]
=> [1,1,0,0,1,0]
=> 1
[3,+,1] => [2,3,1] => [1,1,0,1,0,0]
=> [1,1,0,0,1,0]
=> 1
[+,+,+,+] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> 0
[-,+,+,+] => [2,3,4,1] => [1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 2
[+,-,+,+] => [1,3,4,2] => [1,0,1,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0]
=> 1
[+,+,-,+] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [1,0,1,1,1,0,0,0]
=> 3
[+,+,+,-] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> 0
[-,+,-,+] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> 3
[-,+,+,-] => [2,3,1,4] => [1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
[+,-,+,-] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,0]
=> 4
[+,+,-,-] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> 0
[-,+,-,-] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,0]
=> 3
[+,-,-,-] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> 0
[-,-,-,-] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> 0
[+,+,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [1,0,1,1,1,0,0,0]
=> 3
[-,+,4,3] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> 3
[+,3,2,+] => [1,3,4,2] => [1,0,1,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0]
=> 1
[+,3,2,-] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,0]
=> 4
[+,4,2,3] => [1,3,4,2] => [1,0,1,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0]
=> 1
[+,4,+,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0]
=> 1
[2,1,+,+] => [2,3,4,1] => [1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 2
[2,1,-,+] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> 3
[2,1,+,-] => [2,3,1,4] => [1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
[2,1,-,-] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,0]
=> 3
[2,1,4,3] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> 3
[3,1,2,+] => [2,3,4,1] => [1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 2
[3,1,2,-] => [2,3,1,4] => [1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
[3,1,4,2] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> 3
[3,+,1,+] => [2,3,4,1] => [1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 2
[3,+,1,-] => [2,3,1,4] => [1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
[3,+,4,1] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> 3
[4,1,2,3] => [2,3,4,1] => [1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 2
[4,1,+,2] => [2,3,4,1] => [1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> 2
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
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