- FindStat

Identifier

Mp00103: Dyck paths —peeling map⟶ Dyck paths
St001172: Dyck paths ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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$F_{1} = 1$

$F_{2} = 2$

$F_{3} = 5$

$F_{4} = 14$

$F_{5} = 41 + q$

$F_{6} = 124 + 7\ q + q^{2}$

$F_{7} = 383 + 38\ q + 7\ q^{2} + q^{3}$

$F_{8} = 1202 + 179\ q + 41\ q^{2} + 7\ q^{3} + q^{4}$

Description

The number of 1-rises at odd height of a Dyck path.

Map

peeling map

Description

Send a Dyck path to its peeled Dyck path.