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Identifier

Mp00150: Perfect matchings —to Dyck path⟶ Dyck paths

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[(1,2),(3,4),(5,6),(7,8)] => [1,0,1,0,1,0,1,0]

[(1,3),(2,4),(5,6),(7,8)] => [1,1,0,0,1,0,1,0]

[(1,4),(2,3),(5,6),(7,8)] => [1,1,0,0,1,0,1,0]

[(1,5),(2,3),(4,6),(7,8)] => [1,1,0,1,0,0,1,0]

[(1,6),(2,3),(4,5),(7,8)] => [1,1,0,1,0,0,1,0]

[(1,7),(2,3),(4,5),(6,8)] => [1,1,0,1,0,1,0,0]

[(1,8),(2,3),(4,5),(6,7)] => [1,1,0,1,0,1,0,0]

[(1,8),(2,4),(3,5),(6,7)] => [1,1,1,0,0,1,0,0]

[(1,7),(2,4),(3,5),(6,8)] => [1,1,1,0,0,1,0,0]

[(1,6),(2,4),(3,5),(7,8)] => [1,1,1,0,0,0,1,0]

[(1,5),(2,4),(3,6),(7,8)] => [1,1,1,0,0,0,1,0]

[(1,4),(2,5),(3,6),(7,8)] => [1,1,1,0,0,0,1,0]

[(1,3),(2,5),(4,6),(7,8)] => [1,1,0,1,0,0,1,0]

[(1,2),(3,5),(4,6),(7,8)] => [1,0,1,1,0,0,1,0]

[(1,2),(3,6),(4,5),(7,8)] => [1,0,1,1,0,0,1,0]

[(1,3),(2,6),(4,5),(7,8)] => [1,1,0,1,0,0,1,0]

[(1,4),(2,6),(3,5),(7,8)] => [1,1,1,0,0,0,1,0]

[(1,5),(2,6),(3,4),(7,8)] => [1,1,1,0,0,0,1,0]

[(1,6),(2,5),(3,4),(7,8)] => [1,1,1,0,0,0,1,0]

[(1,7),(2,5),(3,4),(6,8)] => [1,1,1,0,0,1,0,0]

[(1,8),(2,5),(3,4),(6,7)] => [1,1,1,0,0,1,0,0]

[(1,8),(2,6),(3,4),(5,7)] => [1,1,1,0,1,0,0,0]

[(1,7),(2,6),(3,4),(5,8)] => [1,1,1,0,1,0,0,0]

[(1,6),(2,7),(3,4),(5,8)] => [1,1,1,0,1,0,0,0]

[(1,5),(2,7),(3,4),(6,8)] => [1,1,1,0,0,1,0,0]

[(1,4),(2,7),(3,5),(6,8)] => [1,1,1,0,0,1,0,0]

[(1,3),(2,7),(4,5),(6,8)] => [1,1,0,1,0,1,0,0]

[(1,2),(3,7),(4,5),(6,8)] => [1,0,1,1,0,1,0,0]

[(1,2),(3,8),(4,5),(6,7)] => [1,0,1,1,0,1,0,0]

[(1,3),(2,8),(4,5),(6,7)] => [1,1,0,1,0,1,0,0]

[(1,4),(2,8),(3,5),(6,7)] => [1,1,1,0,0,1,0,0]

[(1,5),(2,8),(3,4),(6,7)] => [1,1,1,0,0,1,0,0]

[(1,6),(2,8),(3,4),(5,7)] => [1,1,1,0,1,0,0,0]

[(1,7),(2,8),(3,4),(5,6)] => [1,1,1,0,1,0,0,0]

[(1,8),(2,7),(3,4),(5,6)] => [1,1,1,0,1,0,0,0]

[(1,8),(2,7),(3,5),(4,6)] => [1,1,1,1,0,0,0,0]

[(1,7),(2,8),(3,5),(4,6)] => [1,1,1,1,0,0,0,0]

[(1,6),(2,8),(3,5),(4,7)] => [1,1,1,1,0,0,0,0]

[(1,5),(2,8),(3,6),(4,7)] => [1,1,1,1,0,0,0,0]

[(1,4),(2,8),(3,6),(5,7)] => [1,1,1,0,1,0,0,0]

[(1,3),(2,8),(4,6),(5,7)] => [1,1,0,1,1,0,0,0]

[(1,2),(3,8),(4,6),(5,7)] => [1,0,1,1,1,0,0,0]

[(1,2),(3,7),(4,6),(5,8)] => [1,0,1,1,1,0,0,0]

[(1,3),(2,7),(4,6),(5,8)] => [1,1,0,1,1,0,0,0]

[(1,4),(2,7),(3,6),(5,8)] => [1,1,1,0,1,0,0,0]

[(1,5),(2,7),(3,6),(4,8)] => [1,1,1,1,0,0,0,0]

[(1,6),(2,7),(3,5),(4,8)] => [1,1,1,1,0,0,0,0]

[(1,7),(2,6),(3,5),(4,8)] => [1,1,1,1,0,0,0,0]

[(1,8),(2,6),(3,5),(4,7)] => [1,1,1,1,0,0,0,0]

[(1,8),(2,5),(3,6),(4,7)] => [1,1,1,1,0,0,0,0]

[(1,7),(2,5),(3,6),(4,8)] => [1,1,1,1,0,0,0,0]

[(1,6),(2,5),(3,7),(4,8)] => [1,1,1,1,0,0,0,0]

[(1,5),(2,6),(3,7),(4,8)] => [1,1,1,1,0,0,0,0]

[(1,4),(2,6),(3,7),(5,8)] => [1,1,1,0,1,0,0,0]

[(1,3),(2,6),(4,7),(5,8)] => [1,1,0,1,1,0,0,0]

[(1,2),(3,6),(4,7),(5,8)] => [1,0,1,1,1,0,0,0]

[(1,2),(3,5),(4,7),(6,8)] => [1,0,1,1,0,1,0,0]

[(1,3),(2,5),(4,7),(6,8)] => [1,1,0,1,0,1,0,0]

[(1,4),(2,5),(3,7),(6,8)] => [1,1,1,0,0,1,0,0]

[(1,5),(2,4),(3,7),(6,8)] => [1,1,1,0,0,1,0,0]

[(1,6),(2,4),(3,7),(5,8)] => [1,1,1,0,1,0,0,0]

[(1,7),(2,4),(3,6),(5,8)] => [1,1,1,0,1,0,0,0]

[(1,8),(2,4),(3,6),(5,7)] => [1,1,1,0,1,0,0,0]

[(1,8),(2,3),(4,6),(5,7)] => [1,1,0,1,1,0,0,0]

[(1,7),(2,3),(4,6),(5,8)] => [1,1,0,1,1,0,0,0]

[(1,6),(2,3),(4,7),(5,8)] => [1,1,0,1,1,0,0,0]

[(1,5),(2,3),(4,7),(6,8)] => [1,1,0,1,0,1,0,0]

[(1,4),(2,3),(5,7),(6,8)] => [1,1,0,0,1,1,0,0]

[(1,3),(2,4),(5,7),(6,8)] => [1,1,0,0,1,1,0,0]

[(1,2),(3,4),(5,7),(6,8)] => [1,0,1,0,1,1,0,0]

[(1,2),(3,4),(5,8),(6,7)] => [1,0,1,0,1,1,0,0]

[(1,3),(2,4),(5,8),(6,7)] => [1,1,0,0,1,1,0,0]

[(1,4),(2,3),(5,8),(6,7)] => [1,1,0,0,1,1,0,0]

[(1,5),(2,3),(4,8),(6,7)] => [1,1,0,1,0,1,0,0]

[(1,6),(2,3),(4,8),(5,7)] => [1,1,0,1,1,0,0,0]

[(1,7),(2,3),(4,8),(5,6)] => [1,1,0,1,1,0,0,0]

[(1,8),(2,3),(4,7),(5,6)] => [1,1,0,1,1,0,0,0]

[(1,8),(2,4),(3,7),(5,6)] => [1,1,1,0,1,0,0,0]

[(1,7),(2,4),(3,8),(5,6)] => [1,1,1,0,1,0,0,0]

[(1,6),(2,4),(3,8),(5,7)] => [1,1,1,0,1,0,0,0]

[(1,5),(2,4),(3,8),(6,7)] => [1,1,1,0,0,1,0,0]

[(1,4),(2,5),(3,8),(6,7)] => [1,1,1,0,0,1,0,0]

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Description

The Dyck path corresponding to the opener-closer sequence of the perfect matching.

Properties

surjective, graded

Sage code

def mapping(m):
    n = m.size()
    return DyckWord([1 if m.partner(i) > i else 0 for i in range(1,n+1)])

Weight

Created

Sep 03, 2020 at 14:42 by Martin Rubey

Updated

Sep 03, 2020 at 14:42 by Martin Rubey