- FindStat

Identifier

Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
St001473: Dyck paths ⟶ ℤ

Values

[1,0] => [1,1,0,0] => 1
[1,0,1,0] => [1,1,0,1,0,0] => 4
[1,1,0,0] => [1,1,1,0,0,0] => 1
[1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 4
[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] => 5
[1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => 1
[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] => 4
[1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => 5
[1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => 4
[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] => 4
[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] => 5
[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] => 4
[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] => 6
[1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => 7
[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] => 4
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => 7
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => 7
[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] => 7
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => 5
[1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => 6
[1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 4
[1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => 4
[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => 4
[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] => 4
[1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => 4
[1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => 4
[1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => 4
[1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => 5
[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] => 4
[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] => 6
[1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 5
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => 4
[1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => 4
[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] => 5
[1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => 4
[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] => 6
[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] => 4
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 5
[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] => 7
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[] => [1,0] => 1

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

$F_{1} = q$

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

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

$F_{4} = q + 8\ q^{4} + 4\ q^{5} + q^{6}$

$F_{5} = q + 17\ q^{4} + 13\ q^{5} + 5\ q^{6} + 6\ q^{7}$

Description

The absolute value of the sum of all entries of the Coxeter matrix of the corresponding LNakayama algebra.

Map

prime Dyck path

Description

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