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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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-----------------------------------------------------------------------------
Statistic identifier: St001959
-----------------------------------------------------------------------------
Collection: Dyck paths
-----------------------------------------------------------------------------
Description: The product of the heights of the peaks of a Dyck path.
-----------------------------------------------------------------------------
References: [1] [mathoverflow:480173]
[2] Sum over all Dyck paths of semilength n of products over all peaks p of y_p, where y_p is the y-coordinate of peak p. [[OEIS:A258173]]
-----------------------------------------------------------------------------
Code:
def statistic(D):
return prod(D.heights()[i+1] for i in D.peaks())
-----------------------------------------------------------------------------
Statistic values:
[1,0,1,0] => 1
[1,1,0,0] => 2
[1,0,1,0,1,0] => 1
[1,0,1,1,0,0] => 2
[1,1,0,0,1,0] => 2
[1,1,0,1,0,0] => 4
[1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,0] => 1
[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] => 4
[1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,0] => 8
[1,1,0,1,1,0,0,0] => 6
[1,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,0,0] => 6
[1,1,1,0,1,0,0,0] => 9
[1,1,1,1,0,0,0,0] => 4
[1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0] => 4
[1,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,0] => 8
[1,0,1,1,0,1,1,0,0,0] => 6
[1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,0] => 6
[1,0,1,1,1,0,1,0,0,0] => 9
[1,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,0] => 8
[1,1,0,0,1,1,1,0,0,0] => 6
[1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,0] => 8
[1,1,0,1,0,1,0,0,1,0] => 8
[1,1,0,1,0,1,0,1,0,0] => 16
[1,1,0,1,0,1,1,0,0,0] => 12
[1,1,0,1,1,0,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,0,0] => 12
[1,1,0,1,1,0,1,0,0,0] => 18
[1,1,0,1,1,1,0,0,0,0] => 8
[1,1,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,0] => 6
[1,1,1,0,0,1,0,0,1,0] => 6
[1,1,1,0,0,1,0,1,0,0] => 12
[1,1,1,0,0,1,1,0,0,0] => 9
[1,1,1,0,1,0,0,0,1,0] => 9
[1,1,1,0,1,0,0,1,0,0] => 18
[1,1,1,0,1,0,1,0,0,0] => 27
[1,1,1,0,1,1,0,0,0,0] => 12
[1,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,0] => 8
[1,1,1,1,0,0,1,0,0,0] => 12
[1,1,1,1,0,1,0,0,0,0] => 16
[1,1,1,1,1,0,0,0,0,0] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => 2
[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] => 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] => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => 4
[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] => 8
[1,0,1,0,1,1,0,1,1,0,0,0] => 6
[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] => 6
[1,0,1,0,1,1,1,0,1,0,0,0] => 9
[1,0,1,0,1,1,1,1,0,0,0,0] => 4
[1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,0] => 8
[1,0,1,1,0,0,1,1,1,0,0,0] => 6
[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] => 8
[1,0,1,1,0,1,0,1,0,0,1,0] => 8
[1,0,1,1,0,1,0,1,0,1,0,0] => 16
[1,0,1,1,0,1,0,1,1,0,0,0] => 12
[1,0,1,1,0,1,1,0,0,0,1,0] => 6
[1,0,1,1,0,1,1,0,0,1,0,0] => 12
[1,0,1,1,0,1,1,0,1,0,0,0] => 18
[1,0,1,1,0,1,1,1,0,0,0,0] => 8
[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] => 6
[1,0,1,1,1,0,0,1,0,0,1,0] => 6
[1,0,1,1,1,0,0,1,0,1,0,0] => 12
[1,0,1,1,1,0,0,1,1,0,0,0] => 9
[1,0,1,1,1,0,1,0,0,0,1,0] => 9
[1,0,1,1,1,0,1,0,0,1,0,0] => 18
[1,0,1,1,1,0,1,0,1,0,0,0] => 27
[1,0,1,1,1,0,1,1,0,0,0,0] => 12
[1,0,1,1,1,1,0,0,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,0,1,0,0] => 8
[1,0,1,1,1,1,0,0,1,0,0,0] => 12
[1,0,1,1,1,1,0,1,0,0,0,0] => 16
[1,0,1,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,0,1,1,0,0,1,0] => 4
[1,1,0,0,1,0,1,1,0,1,0,0] => 8
[1,1,0,0,1,0,1,1,1,0,0,0] => 6
[1,1,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,0] => 8
[1,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,0,0,1,1,0,1,0,1,0,0] => 16
[1,1,0,0,1,1,0,1,1,0,0,0] => 12
[1,1,0,0,1,1,1,0,0,0,1,0] => 6
[1,1,0,0,1,1,1,0,0,1,0,0] => 12
[1,1,0,0,1,1,1,0,1,0,0,0] => 18
[1,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,0,1,1,0,0] => 8
[1,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,0,1,0,0,1,1,0,1,0,0] => 16
[1,1,0,1,0,0,1,1,1,0,0,0] => 12
[1,1,0,1,0,1,0,0,1,0,1,0] => 8
[1,1,0,1,0,1,0,0,1,1,0,0] => 16
[1,1,0,1,0,1,0,1,0,0,1,0] => 16
[1,1,0,1,0,1,0,1,0,1,0,0] => 32
[1,1,0,1,0,1,0,1,1,0,0,0] => 24
[1,1,0,1,0,1,1,0,0,0,1,0] => 12
[1,1,0,1,0,1,1,0,0,1,0,0] => 24
[1,1,0,1,0,1,1,0,1,0,0,0] => 36
[1,1,0,1,0,1,1,1,0,0,0,0] => 16
[1,1,0,1,1,0,0,0,1,0,1,0] => 6
[1,1,0,1,1,0,0,0,1,1,0,0] => 12
[1,1,0,1,1,0,0,1,0,0,1,0] => 12
[1,1,0,1,1,0,0,1,0,1,0,0] => 24
[1,1,0,1,1,0,0,1,1,0,0,0] => 18
[1,1,0,1,1,0,1,0,0,0,1,0] => 18
[1,1,0,1,1,0,1,0,0,1,0,0] => 36
[1,1,0,1,1,0,1,0,1,0,0,0] => 54
[1,1,0,1,1,0,1,1,0,0,0,0] => 24
[1,1,0,1,1,1,0,0,0,0,1,0] => 8
[1,1,0,1,1,1,0,0,0,1,0,0] => 16
[1,1,0,1,1,1,0,0,1,0,0,0] => 24
[1,1,0,1,1,1,0,1,0,0,0,0] => 32
[1,1,0,1,1,1,1,0,0,0,0,0] => 10
[1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => 6
[1,1,1,0,0,0,1,1,0,0,1,0] => 6
[1,1,1,0,0,0,1,1,0,1,0,0] => 12
[1,1,1,0,0,0,1,1,1,0,0,0] => 9
[1,1,1,0,0,1,0,0,1,0,1,0] => 6
[1,1,1,0,0,1,0,0,1,1,0,0] => 12
[1,1,1,0,0,1,0,1,0,0,1,0] => 12
[1,1,1,0,0,1,0,1,0,1,0,0] => 24
[1,1,1,0,0,1,0,1,1,0,0,0] => 18
[1,1,1,0,0,1,1,0,0,0,1,0] => 9
[1,1,1,0,0,1,1,0,0,1,0,0] => 18
[1,1,1,0,0,1,1,0,1,0,0,0] => 27
[1,1,1,0,0,1,1,1,0,0,0,0] => 12
[1,1,1,0,1,0,0,0,1,0,1,0] => 9
[1,1,1,0,1,0,0,0,1,1,0,0] => 18
[1,1,1,0,1,0,0,1,0,0,1,0] => 18
[1,1,1,0,1,0,0,1,0,1,0,0] => 36
[1,1,1,0,1,0,0,1,1,0,0,0] => 27
[1,1,1,0,1,0,1,0,0,0,1,0] => 27
[1,1,1,0,1,0,1,0,0,1,0,0] => 54
[1,1,1,0,1,0,1,0,1,0,0,0] => 81
[1,1,1,0,1,0,1,1,0,0,0,0] => 36
[1,1,1,0,1,1,0,0,0,0,1,0] => 12
[1,1,1,0,1,1,0,0,0,1,0,0] => 24
[1,1,1,0,1,1,0,0,1,0,0,0] => 36
[1,1,1,0,1,1,0,1,0,0,0,0] => 48
[1,1,1,0,1,1,1,0,0,0,0,0] => 15
[1,1,1,1,0,0,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,1,0,0,0,1,0,0,1,0] => 8
[1,1,1,1,0,0,0,1,0,1,0,0] => 16
[1,1,1,1,0,0,0,1,1,0,0,0] => 12
[1,1,1,1,0,0,1,0,0,0,1,0] => 12
[1,1,1,1,0,0,1,0,0,1,0,0] => 24
[1,1,1,1,0,0,1,0,1,0,0,0] => 36
[1,1,1,1,0,0,1,1,0,0,0,0] => 16
[1,1,1,1,0,1,0,0,0,0,1,0] => 16
[1,1,1,1,0,1,0,0,0,1,0,0] => 32
[1,1,1,1,0,1,0,0,1,0,0,0] => 48
[1,1,1,1,0,1,0,1,0,0,0,0] => 64
[1,1,1,1,0,1,1,0,0,0,0,0] => 20
[1,1,1,1,1,0,0,0,0,0,1,0] => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => 10
[1,1,1,1,1,0,0,0,1,0,0,0] => 15
[1,1,1,1,1,0,0,1,0,0,0,0] => 20
[1,1,1,1,1,0,1,0,0,0,0,0] => 25
[1,1,1,1,1,1,0,0,0,0,0,0] => 6
-----------------------------------------------------------------------------
Created: Oct 07, 2024 at 09:04 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Oct 07, 2024 at 09:04 by Martin Rubey