- FindStat

Identifier

Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
St001492: Dyck paths ⟶ ℤ

Values

[1,0] => [1,1,0,0] => 3

[1,0,1,0] => [1,1,0,1,0,0] => 3

[1,1,0,0] => [1,1,1,0,0,0] => 4

[1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 3

[1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 4

[1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 4

[1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => 4

[1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => 5

[1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => 4

[1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => 4

[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => 5

[1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 4

[1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 5

[1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => 4

[1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => 5

[1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => 4

[1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => 4

[1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => 5

[1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => 5

[1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 5

[1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 5

[1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 6

[1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 5

[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 5

[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 5

[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => 5

[1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => 5

[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 5

[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 6

[1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 4

[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => 5

[1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => 5

[1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 5

[1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 6

[1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 5

[1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 6

[1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 5

[1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 5

[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 6

[1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => 5

[1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => 6

[1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 5

[1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 5

[1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 5

[1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 4

[1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => 5

[1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => 6

[1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => 5

[1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => 5

[1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 6

[1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 5

[1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 6

[1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 5

[1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => 5

[1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => 6

[1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 5

[1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => 5

[1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => 5

[1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 6

[1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 6

[1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 6

[1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 6

[1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 6

[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 7

[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 6

[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 6

[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 6

[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 6

[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 6

[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 5

[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 6

[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 5

[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 6

[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 6

[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 5

[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 6

[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 6

[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 6

[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 6

[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 6

[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 7

[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 6

[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 7

[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 5

[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 5

[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 6

[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 5

[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 6

[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 6

[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 5

[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 6

[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 6

[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 5

[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 6

[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 6

[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 6

[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 7

[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 5

[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 5

[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 6

[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 6

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$F_{1} = q^{3}$

$F_{2} = q^{3} + q^{4}$

$F_{3} = q^{3} + 3\ q^{4} + q^{5}$

$F_{4} = 6\ q^{4} + 7\ q^{5} + q^{6}$

$F_{5} = 2\ q^{4} + 25\ q^{5} + 14\ q^{6} + q^{7}$

$F_{6} = 22\ q^{5} + 83\ q^{6} + 26\ q^{7} + q^{8}$

Description

The number of simple modules that do not appear in the socle of the regular module or have no nontrivial selfextensions with the regular module in the corresponding Nakayama algebra.

Map

prime Dyck path

Description

Return the Dyck path obtained by adding an initial up and a final down step.