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Identifier

St001836: Perfect matchings ⟶ ℤ

Values

[(1,2)] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[(1,6),(2,4),(3,5),(7,8)] => 10

[(1,5),(2,4),(3,6),(7,8)] => 10

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

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

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

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

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

[(1,4),(2,6),(3,5),(7,8)] => 9

[(1,5),(2,6),(3,4),(7,8)] => 10

[(1,6),(2,5),(3,4),(7,8)] => 12

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[(1,5),(2,4),(3,7),(6,8)] => 10

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[(1,5),(2,4),(3,8),(6,7)] => 10

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

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Description

The number of occurrences of a 213 pattern in the restricted growth word of a perfect matching.

Code

def to_standard(s):
    a = {e: i for i, e in enumerate(sorted(set(s)))}
    return [a[e] for e in s]
    
def pattern_occurrences(w, pat):
    pat = to_standard(pat)
    return sum(1 for s in Subwords(w, len(pat))
               if pat == to_standard(s))

def statistic(m):
    return pattern_occurrences(m.to_restricted_growth_word(), [2,1,3])

Created

Sep 30, 2022 at 17:05 by Martin Rubey

Updated

Sep 30, 2022 at 17:05 by Martin Rubey