Identifier
- St000161: Binary trees ⟶ ℤ
Values
=>
Cc0010;cc-rep
[.,.]=>0
[.,[.,.]]=>1
[[.,.],.]=>0
[.,[.,[.,.]]]=>3
[.,[[.,.],.]]=>2
[[.,.],[.,.]]=>1
[[.,[.,.]],.]=>1
[[[.,.],.],.]=>0
[.,[.,[.,[.,.]]]]=>6
[.,[.,[[.,.],.]]]=>5
[.,[[.,.],[.,.]]]=>4
[.,[[.,[.,.]],.]]=>4
[.,[[[.,.],.],.]]=>3
[[.,.],[.,[.,.]]]=>3
[[.,.],[[.,.],.]]=>2
[[.,[.,.]],[.,.]]=>2
[[[.,.],.],[.,.]]=>1
[[.,[.,[.,.]]],.]=>3
[[.,[[.,.],.]],.]=>2
[[[.,.],[.,.]],.]=>1
[[[.,[.,.]],.],.]=>1
[[[[.,.],.],.],.]=>0
[.,[.,[.,[.,[.,.]]]]]=>10
[.,[.,[.,[[.,.],.]]]]=>9
[.,[.,[[.,.],[.,.]]]]=>8
[.,[.,[[.,[.,.]],.]]]=>8
[.,[.,[[[.,.],.],.]]]=>7
[.,[[.,.],[.,[.,.]]]]=>7
[.,[[.,.],[[.,.],.]]]=>6
[.,[[.,[.,.]],[.,.]]]=>6
[.,[[[.,.],.],[.,.]]]=>5
[.,[[.,[.,[.,.]]],.]]=>7
[.,[[.,[[.,.],.]],.]]=>6
[.,[[[.,.],[.,.]],.]]=>5
[.,[[[.,[.,.]],.],.]]=>5
[.,[[[[.,.],.],.],.]]=>4
[[.,.],[.,[.,[.,.]]]]=>6
[[.,.],[.,[[.,.],.]]]=>5
[[.,.],[[.,.],[.,.]]]=>4
[[.,.],[[.,[.,.]],.]]=>4
[[.,.],[[[.,.],.],.]]=>3
[[.,[.,.]],[.,[.,.]]]=>4
[[.,[.,.]],[[.,.],.]]=>3
[[[.,.],.],[.,[.,.]]]=>3
[[[.,.],.],[[.,.],.]]=>2
[[.,[.,[.,.]]],[.,.]]=>4
[[.,[[.,.],.]],[.,.]]=>3
[[[.,.],[.,.]],[.,.]]=>2
[[[.,[.,.]],.],[.,.]]=>2
[[[[.,.],.],.],[.,.]]=>1
[[.,[.,[.,[.,.]]]],.]=>6
[[.,[.,[[.,.],.]]],.]=>5
[[.,[[.,.],[.,.]]],.]=>4
[[.,[[.,[.,.]],.]],.]=>4
[[.,[[[.,.],.],.]],.]=>3
[[[.,.],[.,[.,.]]],.]=>3
[[[.,.],[[.,.],.]],.]=>2
[[[.,[.,.]],[.,.]],.]=>2
[[[[.,.],.],[.,.]],.]=>1
[[[.,[.,[.,.]]],.],.]=>3
[[[.,[[.,.],.]],.],.]=>2
[[[[.,.],[.,.]],.],.]=>1
[[[[.,[.,.]],.],.],.]=>1
[[[[[.,.],.],.],.],.]=>0
[.,[.,[.,[.,[.,[.,.]]]]]]=>15
[.,[.,[.,[.,[[.,.],.]]]]]=>14
[.,[.,[.,[[.,.],[.,.]]]]]=>13
[.,[.,[.,[[.,[.,.]],.]]]]=>13
[.,[.,[.,[[[.,.],.],.]]]]=>12
[.,[.,[[.,.],[.,[.,.]]]]]=>12
[.,[.,[[.,.],[[.,.],.]]]]=>11
[.,[.,[[.,[.,.]],[.,.]]]]=>11
[.,[.,[[[.,.],.],[.,.]]]]=>10
[.,[.,[[.,[.,[.,.]]],.]]]=>12
[.,[.,[[.,[[.,.],.]],.]]]=>11
[.,[.,[[[.,.],[.,.]],.]]]=>10
[.,[.,[[[.,[.,.]],.],.]]]=>10
[.,[.,[[[[.,.],.],.],.]]]=>9
[.,[[.,.],[.,[.,[.,.]]]]]=>11
[.,[[.,.],[.,[[.,.],.]]]]=>10
[.,[[.,.],[[.,.],[.,.]]]]=>9
[.,[[.,.],[[.,[.,.]],.]]]=>9
[.,[[.,.],[[[.,.],.],.]]]=>8
[.,[[.,[.,.]],[.,[.,.]]]]=>9
[.,[[.,[.,.]],[[.,.],.]]]=>8
[.,[[[.,.],.],[.,[.,.]]]]=>8
[.,[[[.,.],.],[[.,.],.]]]=>7
[.,[[.,[.,[.,.]]],[.,.]]]=>9
[.,[[.,[[.,.],.]],[.,.]]]=>8
[.,[[[.,.],[.,.]],[.,.]]]=>7
[.,[[[.,[.,.]],.],[.,.]]]=>7
[.,[[[[.,.],.],.],[.,.]]]=>6
[.,[[.,[.,[.,[.,.]]]],.]]=>11
[.,[[.,[.,[[.,.],.]]],.]]=>10
[.,[[.,[[.,.],[.,.]]],.]]=>9
[.,[[.,[[.,[.,.]],.]],.]]=>9
[.,[[.,[[[.,.],.],.]],.]]=>8
[.,[[[.,.],[.,[.,.]]],.]]=>8
[.,[[[.,.],[[.,.],.]],.]]=>7
[.,[[[.,[.,.]],[.,.]],.]]=>7
[.,[[[[.,.],.],[.,.]],.]]=>6
[.,[[[.,[.,[.,.]]],.],.]]=>8
[.,[[[.,[[.,.],.]],.],.]]=>7
[.,[[[[.,.],[.,.]],.],.]]=>6
[.,[[[[.,[.,.]],.],.],.]]=>6
[.,[[[[[.,.],.],.],.],.]]=>5
[[.,.],[.,[.,[.,[.,.]]]]]=>10
[[.,.],[.,[.,[[.,.],.]]]]=>9
[[.,.],[.,[[.,.],[.,.]]]]=>8
[[.,.],[.,[[.,[.,.]],.]]]=>8
[[.,.],[.,[[[.,.],.],.]]]=>7
[[.,.],[[.,.],[.,[.,.]]]]=>7
[[.,.],[[.,.],[[.,.],.]]]=>6
[[.,.],[[.,[.,.]],[.,.]]]=>6
[[.,.],[[[.,.],.],[.,.]]]=>5
[[.,.],[[.,[.,[.,.]]],.]]=>7
[[.,.],[[.,[[.,.],.]],.]]=>6
[[.,.],[[[.,.],[.,.]],.]]=>5
[[.,.],[[[.,[.,.]],.],.]]=>5
[[.,.],[[[[.,.],.],.],.]]=>4
[[.,[.,.]],[.,[.,[.,.]]]]=>7
[[.,[.,.]],[.,[[.,.],.]]]=>6
[[.,[.,.]],[[.,.],[.,.]]]=>5
[[.,[.,.]],[[.,[.,.]],.]]=>5
[[.,[.,.]],[[[.,.],.],.]]=>4
[[[.,.],.],[.,[.,[.,.]]]]=>6
[[[.,.],.],[.,[[.,.],.]]]=>5
[[[.,.],.],[[.,.],[.,.]]]=>4
[[[.,.],.],[[.,[.,.]],.]]=>4
[[[.,.],.],[[[.,.],.],.]]=>3
[[.,[.,[.,.]]],[.,[.,.]]]=>6
[[.,[.,[.,.]]],[[.,.],.]]=>5
[[.,[[.,.],.]],[.,[.,.]]]=>5
[[.,[[.,.],.]],[[.,.],.]]=>4
[[[.,.],[.,.]],[.,[.,.]]]=>4
[[[.,.],[.,.]],[[.,.],.]]=>3
[[[.,[.,.]],.],[.,[.,.]]]=>4
[[[.,[.,.]],.],[[.,.],.]]=>3
[[[[.,.],.],.],[.,[.,.]]]=>3
[[[[.,.],.],.],[[.,.],.]]=>2
[[.,[.,[.,[.,.]]]],[.,.]]=>7
[[.,[.,[[.,.],.]]],[.,.]]=>6
[[.,[[.,.],[.,.]]],[.,.]]=>5
[[.,[[.,[.,.]],.]],[.,.]]=>5
[[.,[[[.,.],.],.]],[.,.]]=>4
[[[.,.],[.,[.,.]]],[.,.]]=>4
[[[.,.],[[.,.],.]],[.,.]]=>3
[[[.,[.,.]],[.,.]],[.,.]]=>3
[[[[.,.],.],[.,.]],[.,.]]=>2
[[[.,[.,[.,.]]],.],[.,.]]=>4
[[[.,[[.,.],.]],.],[.,.]]=>3
[[[[.,.],[.,.]],.],[.,.]]=>2
[[[[.,[.,.]],.],.],[.,.]]=>2
[[[[[.,.],.],.],.],[.,.]]=>1
[[.,[.,[.,[.,[.,.]]]]],.]=>10
[[.,[.,[.,[[.,.],.]]]],.]=>9
[[.,[.,[[.,.],[.,.]]]],.]=>8
[[.,[.,[[.,[.,.]],.]]],.]=>8
[[.,[.,[[[.,.],.],.]]],.]=>7
[[.,[[.,.],[.,[.,.]]]],.]=>7
[[.,[[.,.],[[.,.],.]]],.]=>6
[[.,[[.,[.,.]],[.,.]]],.]=>6
[[.,[[[.,.],.],[.,.]]],.]=>5
[[.,[[.,[.,[.,.]]],.]],.]=>7
[[.,[[.,[[.,.],.]],.]],.]=>6
[[.,[[[.,.],[.,.]],.]],.]=>5
[[.,[[[.,[.,.]],.],.]],.]=>5
[[.,[[[[.,.],.],.],.]],.]=>4
[[[.,.],[.,[.,[.,.]]]],.]=>6
[[[.,.],[.,[[.,.],.]]],.]=>5
[[[.,.],[[.,.],[.,.]]],.]=>4
[[[.,.],[[.,[.,.]],.]],.]=>4
[[[.,.],[[[.,.],.],.]],.]=>3
[[[.,[.,.]],[.,[.,.]]],.]=>4
[[[.,[.,.]],[[.,.],.]],.]=>3
[[[[.,.],.],[.,[.,.]]],.]=>3
[[[[.,.],.],[[.,.],.]],.]=>2
[[[.,[.,[.,.]]],[.,.]],.]=>4
[[[.,[[.,.],.]],[.,.]],.]=>3
[[[[.,.],[.,.]],[.,.]],.]=>2
[[[[.,[.,.]],.],[.,.]],.]=>2
[[[[[.,.],.],.],[.,.]],.]=>1
[[[.,[.,[.,[.,.]]]],.],.]=>6
[[[.,[.,[[.,.],.]]],.],.]=>5
[[[.,[[.,.],[.,.]]],.],.]=>4
[[[.,[[.,[.,.]],.]],.],.]=>4
[[[.,[[[.,.],.],.]],.],.]=>3
[[[[.,.],[.,[.,.]]],.],.]=>3
[[[[.,.],[[.,.],.]],.],.]=>2
[[[[.,[.,.]],[.,.]],.],.]=>2
[[[[[.,.],.],[.,.]],.],.]=>1
[[[[.,[.,[.,.]]],.],.],.]=>3
[[[[.,[[.,.],.]],.],.],.]=>2
[[[[[.,.],[.,.]],.],.],.]=>1
[[[[[.,[.,.]],.],.],.],.]=>1
[[[[[[.,.],.],.],.],.],.]=>0
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>10
[.,[[[.,.],[.,.]],[[.,.],.]]]=>9
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>11
[.,[[.,[[[.,.],.],.]],[.,.]]]=>10
[.,[[[.,.],[[.,.],.]],[.,.]]]=>9
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>9
[.,[[[[.,.],.],[.,.]],[.,.]]]=>8
[.,[[[.,[[.,.],.]],.],[.,.]]]=>9
[.,[[[[.,.],[.,.]],.],[.,.]]]=>8
[.,[[[[.,[.,.]],.],.],[.,.]]]=>8
[.,[[[[[.,.],.],.],.],[.,.]]]=>7
[.,[[.,[[[[.,.],.],.],.]],.]]=>10
[.,[[[[.,.],[.,.]],[.,.]],.]]=>8
[.,[[[[[.,.],.],.],[.,.]],.]]=>7
[.,[[[.,[[.,[.,.]],.]],.],.]]=>10
[.,[[[.,[[[.,.],.],.]],.],.]]=>9
[.,[[[[.,.],[[.,.],.]],.],.]]=>8
[.,[[[[.,[.,.]],[.,.]],.],.]]=>8
[.,[[[[[.,.],.],[.,.]],.],.]]=>7
[.,[[[[.,[.,[.,.]]],.],.],.]]=>9
[.,[[[[.,[[.,.],.]],.],.],.]]=>8
[.,[[[[[.,.],[.,.]],.],.],.]]=>7
[.,[[[[[.,[.,.]],.],.],.],.]]=>7
[.,[[[[[[.,.],.],.],.],.],.]]=>6
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>15
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>14
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>13
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>13
[[.,.],[.,[.,[[[.,.],.],.]]]]=>12
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>12
[[.,.],[.,[[.,.],[[.,.],.]]]]=>11
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>11
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>12
[[.,.],[.,[[.,[[.,.],.]],.]]]=>11
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>11
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>11
[[.,.],[[[[[.,.],.],.],.],.]]=>5
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>11
[[.,[[[.,.],.],.]],[.,[.,.]]]=>6
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>6
[[[.,.],[.,[.,.]]],[[.,.],.]]=>5
[[[.,[[.,.],.]],.],[.,[.,.]]]=>5
[[[[.,[.,.]],.],.],[.,[.,.]]]=>4
[[[[[.,.],.],.],.],[.,[.,.]]]=>3
[[[[[.,.],.],.],.],[[.,.],.]]=>2
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>11
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>8
[[.,[[[[.,.],.],.],.]],[.,.]]=>5
[[[.,.],[.,[[.,.],.]]],[.,.]]=>6
[[[.,.],[[.,[.,.]],.]],[.,.]]=>5
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>5
[[[[.,.],.],[.,[.,.]]],[.,.]]=>4
[[[[[.,.],.],.],[.,.]],[.,.]]=>2
[[[.,[[.,[.,.]],.]],.],[.,.]]=>5
[[[.,[[[.,.],.],.]],.],[.,.]]=>4
[[[[.,.],[.,[.,.]]],.],[.,.]]=>4
[[[[.,.],[[.,.],.]],.],[.,.]]=>3
[[[[.,[.,.]],[.,.]],.],[.,.]]=>3
[[[[[.,.],.],[.,.]],.],[.,.]]=>2
[[[[.,[.,[.,.]]],.],.],[.,.]]=>4
[[[[.,[[.,.],.]],.],.],[.,.]]=>3
[[[[[.,.],[.,.]],.],.],[.,.]]=>2
[[[[[.,[.,.]],.],.],.],[.,.]]=>2
[[[[[[.,.],.],.],.],.],[.,.]]=>1
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>15
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>14
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>13
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>13
[[.,[.,[.,[[[.,.],.],.]]]],.]=>12
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>12
[[.,[.,[[.,.],[[.,.],.]]]],.]=>11
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>11
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>12
[[.,[.,[[.,[[.,.],.]],.]]],.]=>11
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>11
[[.,[[[.,.],[.,.]],[.,.]]],.]=>7
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>11
[[[[.,.],[.,[.,.]]],[.,.]],.]=>4
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>14
[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>13
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>12
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>12
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>11
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>10
[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>10
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>10
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>12
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>14
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>16
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>16
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>14
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>12
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>12
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>10
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>10
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>8
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>10
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>9
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>8
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>8
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>7
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>21
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>20
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>19
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>19
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>18
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>18
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>18
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>12
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>12
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>12
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>10
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>12
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>11
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>10
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>12
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>10
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>8
[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>8
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>8
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>8
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>12
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>12
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>8
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>8
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>6
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>12
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>12
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>10
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>11
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>10
[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>9
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>10
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>8
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>8
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>8
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>7
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>10
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>10
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>8
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>8
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>6
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>12
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>11
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>10
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>10
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>9
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>8
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>8
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>8
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>7
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>8
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>7
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>6
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>9
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>8
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>6
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>6
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>4
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>12
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>10
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>8
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>8
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>8
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>8
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>6
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>9
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>8
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>7
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>6
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>6
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>6
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>5
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>4
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>6
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>5
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>4
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>6
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>5
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>4
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>8
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>8
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>6
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>5
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>4
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>5
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>4
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>5
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>4
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>6
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>5
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>4
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>5
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>4
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>6
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>4
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>2
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>10
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>8
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>6
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>6
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>5
[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>5
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>4
[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>5
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>4
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>4
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>6
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>5
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>4
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>4
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>2
[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>7
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>2
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>4
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>2
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>4
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[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>26
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[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]=>20
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[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]=>16
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[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]=>16
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]=>16
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[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>20
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[.,[[[.,[[.,.],[.,.]]],.],[[.,.],[.,.]]]]=>17
[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]]=>19
[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]]=>17
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[[.,[.,.]],[[.,[[[.,.],[.,.]],[.,.]]],.]]=>15
[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]]=>13
[[.,[.,.]],[[[.,[[.,.],[.,.]]],.],[.,.]]]=>13
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[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]=>14
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[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>36
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[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>35
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[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>11
[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>9
[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>9
[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>7
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[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>9
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>9
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>7
[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>11
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[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>7
[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>7
[[[[.,.],[.,.]],[[.,.],.]],[[.,.],[.,[.,.]]]]=>10
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[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>1
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[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>45
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>45
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]=>30
[[.,.],[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]]=>30
[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]]=>28
[[.,.],[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]]=>30
[[.,.],[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]]=>30
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]]=>26
[[.,.],[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]]=>26
[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]]=>26
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[[.,.],[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]]=>30
[[.,.],[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]]=>30
[[.,.],[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]]=>28
[[.,.],[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]]=>30
[[.,.],[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]]=>30
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]]=>24
[[.,.],[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]]=>24
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]]=>22
[[.,.],[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]]=>24
[[.,.],[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]]=>24
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]]=>22
[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]]=>22
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]]=>22
[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]]=>22
[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]]=>24
[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]]=>24
[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]]=>22
[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]]=>24
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]]=>24
[[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]]=>30
[[.,.],[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]]=>30
[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]]=>28
[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]]=>30
[[.,.],[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]]=>30
[[.,.],[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]]=>26
[[.,.],[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]]=>26
[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]]=>26
[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]]=>26
[[.,.],[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]]=>30
[[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]]=>30
[[.,.],[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]]=>28
[[.,.],[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]]=>30
[[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]]=>30
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>22
[[.,[[.,.],.]],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]=>22
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]=>20
[[.,[[.,.],.]],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]=>22
[[.,[[.,.],.]],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]=>22
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]=>18
[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]=>18
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]=>18
[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]=>18
[[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]=>22
[[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]=>22
[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]=>20
[[.,[[.,.],.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]=>22
[[.,[[.,.],.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]=>22
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],[[.,.],.]]]]=>18
[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,[[.,.],.]],.]]]=>18
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],[[.,.],.]]]=>16
[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]]=>18
[[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]]=>18
[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],[[.,.],.]]]]=>18
[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,[[.,.],.]],.]]]=>18
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],[[.,.],.]]]=>16
[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],[[.,.],.]]],.]]=>18
[[.,[[.,[[.,.],.]],.]],[[.,[[.,[[.,.],.]],.]],.]]=>18
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]]=>18
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]]=>18
[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],[[.,.],.]]]=>18
[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]]=>18
[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],[[.,.],.]]]=>16
[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,[[.,.],.]],.]]=>16
[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],[[.,.],.]]]=>18
[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,[[.,.],.]],.]]=>18
[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],[[.,.],.]]]=>18
[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[[.,.],.]],.]]=>18
[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]]=>22
[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]]=>22
[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]]=>20
[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]]=>22
[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]]=>22
[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],[[.,.],.]]=>18
[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[[.,.],.]]=>18
[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],[[.,.],.]]=>18
[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],[[.,.],.]]=>18
[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],[[.,.],.]]=>22
[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],[[.,.],.]]=>22
[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],[[.,.],.]]=>20
[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],[[.,.],.]]=>22
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[[.,.],.]]=>22
[[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.]=>30
[[.,[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]],.]=>30
[[.,[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]],.]=>28
[[.,[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]],.]=>30
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[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>16
[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]]=>16
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]]=>14
[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>18
[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>16
[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>14
[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>14
[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>12
[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>14
[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>12
[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>12
[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>10
[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]]=>14
[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>12
[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>10
[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>10
[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>8
[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]]=>18
[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]]=>16
[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>14
[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]]=>14
[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]]=>12
[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>12
[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]=>10
[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>10
[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>8
[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]]=>12
[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]]=>10
[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>8
[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]]=>8
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Description
The sum of the sizes of the right subtrees of a binary tree.
This statistic corresponds to St000012The area of a Dyck path. under the Tamari Dyck path-binary tree bijection, and to St000018The number of inversions of a permutation. of the $312$-avoiding permutation corresponding to the binary tree.
It is also the sum of all heights $j$ of the coordinates $(i,j)$ of the Dyck path corresponding to the binary tree.
This statistic corresponds to St000012The area of a Dyck path. under the Tamari Dyck path-binary tree bijection, and to St000018The number of inversions of a permutation. of the $312$-avoiding permutation corresponding to the binary tree.
It is also the sum of all heights $j$ of the coordinates $(i,j)$ of the Dyck path corresponding to the binary tree.
Code
def statistic(t): if not t: return 0 return statistic(t[0]) + statistic(t[1]) + t[1].node_number()
Created
Sep 20, 2013 at 14:03 by Viviane Pons
Updated
Jan 12, 2018 at 12:45 by Christian Stump
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