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Identifier

Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations

Images

[] => []

[1,0] => [1]

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

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

[1,0,1,0,1,0] => [1,2,3]

[1,0,1,1,0,0] => [1,3,2]

[1,1,0,0,1,0] => [2,1,3]

[1,1,0,1,0,0] => [2,3,1]

[1,1,1,0,0,0] => [3,2,1]

[1,0,1,0,1,0,1,0] => [1,2,3,4]

[1,0,1,0,1,1,0,0] => [1,2,4,3]

[1,0,1,1,0,0,1,0] => [1,3,2,4]

[1,0,1,1,0,1,0,0] => [1,3,4,2]

[1,0,1,1,1,0,0,0] => [1,4,3,2]

[1,1,0,0,1,0,1,0] => [2,1,3,4]

[1,1,0,0,1,1,0,0] => [2,1,4,3]

[1,1,0,1,0,0,1,0] => [2,3,1,4]

[1,1,0,1,0,1,0,0] => [2,3,4,1]

[1,1,0,1,1,0,0,0] => [2,4,3,1]

[1,1,1,0,0,0,1,0] => [3,2,1,4]

[1,1,1,0,0,1,0,0] => [3,2,4,1]

[1,1,1,0,1,0,0,0] => [3,4,2,1]

[1,1,1,1,0,0,0,0] => [4,3,2,1]

[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5]

[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4]

[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5]

[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3]

[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3]

[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5]

[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4]

[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5]

[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2]

[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2]

[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5]

[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2]

[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2]

[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2]

[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5]

[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4]

[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5]

[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3]

[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3]

[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5]

[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4]

[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5]

[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1]

[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1]

[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5]

[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1]

[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1]

[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1]

[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5]

[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4]

[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5]

[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1]

[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1]

[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5]

[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1]

[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1]

[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1]

[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5]

[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1]

[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1]

[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1]

[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1]

[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6]

[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5]

[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6]

[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4]

[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4]

[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6]

[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5]

[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6]

[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3]

[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3]

[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6]

[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3]

[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3]

[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3]

[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6]

[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5]

[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6]

[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4]

[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4]

[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6]

[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5]

[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6]

[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2]

[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2]

[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6]

[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2]

[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2]

[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2]

[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6]

[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5]

[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6]

[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2]

[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2]

[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6]

[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2]

[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2]

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Description

Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).

References

[1] Bandlow, J., Killpatrick, K. An area-to-inv bijection between Dyck paths and 312-avoiding permutations MathSciNet:1877659

Properties

injective, graded

Sage code

def mapping(elt):
    return elt.to_312_avoiding_permutation()

Weight

Created

Jan 19, 2020 at 07:28 by FindStatCrew

Updated

Jan 19, 2020 at 07:28 by Martin Rubey