- FindStat

Identifier

Mp00103: Dyck paths —peeling map⟶ Dyck paths
St001295: Dyck paths ⟶ ℤ (values match St000012The area of a Dyck path.)

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] => 1

[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] => 1

[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] => 1

[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] => 1

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

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

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

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

[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] => 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] => 1

[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] => 1

[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] => 1

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$F_{1} = 1$

$F_{2} = 2$

$F_{3} = 5$

$F_{4} = 13 + q$

$F_{5} = 34 + 6\ q + q^{2} + q^{3}$

$F_{6} = 89 + 25\ q + 7\ q^{2} + 7\ q^{3} + 2\ q^{4} + q^{5} + q^{6}$

Description

Gives the vector space dimension of the homomorphism space between J^2 and J^2.

Map

peeling map

Description

Send a Dyck path to its peeled Dyck path.