- FindStat

Identifier

Mp00103: Dyck paths —peeling map⟶ Dyck paths
St000015: Dyck paths ⟶ ℤ (values match St000053The number of valleys of the Dyck path., St001068Number of torsionless simple modules in the corresponding Nakayama algebra., St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra.)

Values

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

[1,0,1,0] => [1,0,1,0] => 2

[1,1,0,0] => [1,0,1,0] => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The number of peaks of a Dyck path.

Map

peeling map

Description

Send a Dyck path to its peeled Dyck path.