- FindStat

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Identifier

St000053: Dyck paths ⟶ ℤ (values match St000015The number of peaks of a 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] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 625 entries. <<<

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Description

The number of valleys of the Dyck path.

Code

def statistic(r):
    return r.number_of_valleys()

Created

Mar 25, 2013 at 17:36 by Jessica Striker

Updated

Feb 17, 2015 at 17:43 by Martin Rubey