- FindStat

edit this statistic or download as text // json

Identifier

St000678: Dyck paths ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

[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] => 3

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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] => 1

[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] => 4

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

[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] => 4

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

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

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

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

[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] => 3

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

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

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

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

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

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

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

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

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

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

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

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

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

[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

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

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

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

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

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

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

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

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

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

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

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

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

[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] => 1

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

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

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

[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] => 1

[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] => 1

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

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

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

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

[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] => 1

[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] => 1

[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] => 1

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

>>> Load all 1200 entries. <<<

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

Description

The number of up steps after the last double rise of a Dyck path.

References

[1] Adin, R. M., Bagno, E., Roichman, Y. Block decomposition of permutations and Schur-positivity arXiv:1611.06979

Code

def statistic(D):
    i = 0
    j = 0
    for j in range(1,len(D)):
        if D[-j] == 1:
            i += 1
            if D[-j-1] == 1:
                return i
    return i+1

Created

Jan 02, 2017 at 00:13 by Martin Rubey

Updated

Jan 02, 2017 at 00:13 by Martin Rubey