Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000198
Mapping
Mp00018: Binary trees —left border symmetry⟶ Binary trees
Mp00016: Binary trees —left-right symmetry⟶ Binary trees
St000198: Binary trees ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[.,.]
 => [.,.]
 => [.,.]
 => 2
[.,[.,.]]
 => [.,[.,.]]
 => [[.,.],.]
 => 12
[[.,.],.]
 => [[.,.],.]
 => [.,[.,.]]
 => 10
[.,[.,[.,.]]]
 => [.,[.,[.,.]]]
 => [[[.,.],.],.]
 => 56
[.,[[.,.],.]]
 => [.,[[.,.],.]]
 => [[.,[.,.]],.]
 => 52
[[.,.],[.,.]]
 => [[.,[.,.]],.]
 => [.,[[.,.],.]]
 => 44
[[.,[.,.]],.]
 => [[.,.],[.,.]]
 => [[.,.],[.,.]]
 => 50
[[[.,.],.],.]
 => [[[.,.],.],.]
 => [.,[.,[.,.]]]
 => 42
[.,[.,[.,[.,.]]]]
 => [.,[.,[.,[.,.]]]]
 => [[[[.,.],.],.],.]
 => 240
[.,[.,[[.,.],.]]]
 => [.,[.,[[.,.],.]]]
 => [[[.,[.,.]],.],.]
 => 232
[.,[[.,.],[.,.]]]
 => [.,[[.,[.,.]],.]]
 => [[.,[[.,.],.]],.]
 => 216
[.,[[.,[.,.]],.]]
 => [.,[[.,.],[.,.]]]
 => [[[.,.],[.,.]],.]
 => 228
[.,[[[.,.],.],.]]
 => [.,[[[.,.],.],.]]
 => [[.,[.,[.,.]]],.]
 => 212
[[.,.],[.,[.,.]]]
 => [[.,[.,[.,.]]],.]
 => [.,[[[.,.],.],.]]
 => 184
[[.,.],[[.,.],.]]
 => [[.,[[.,.],.]],.]
 => [.,[[.,[.,.]],.]]
 => 180
[[.,[.,.]],[.,.]]
 => [[.,[.,.]],[.,.]]
 => [[.,.],[[.,.],.]]
 => 204
[[[.,.],.],[.,.]]
 => [[[.,[.,.]],.],.]
 => [.,[.,[[.,.],.]]]
 => 172
[[.,[.,[.,.]]],.]
 => [[.,.],[.,[.,.]]]
 => [[[.,.],.],[.,.]]
 => 226
[[.,[[.,.],.]],.]
 => [[.,.],[[.,.],.]]
 => [[.,[.,.]],[.,.]]
 => 210
[[[.,.],[.,.]],.]
 => [[[.,.],[.,.]],.]
 => [.,[[.,.],[.,.]]]
 => 178
[[[.,[.,.]],.],.]
 => [[[.,.],.],[.,.]]
 => [[.,.],[.,[.,.]]]
 => 202
[[[[.,.],.],.],.]
 => [[[[.,.],.],.],.]
 => [.,[.,[.,[.,.]]]]
 => 170
Description
A decimal representation of a binary tree as a code word. Code word constructed by mapping a binary tree to its corresponding set of matching parentheses and then replacing every '''''(''''' with a $1$ and every ''''')''''' with a $0$. We then convert the resulting binary code word to a decimal number.
Matching statistic: St000289
Mapping
Mp00020: Binary trees —to Tamari-corresponding Dyck path⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
St000289: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[.,.]
 => [1,0]
 => 10 => 2
[.,[.,.]]
 => [1,1,0,0]
 => 1100 => 12
[[.,.],.]
 => [1,0,1,0]
 => 1010 => 10
[.,[.,[.,.]]]
 => [1,1,1,0,0,0]
 => 111000 => 56
[.,[[.,.],.]]
 => [1,1,0,1,0,0]
 => 110100 => 52
[[.,.],[.,.]]
 => [1,0,1,1,0,0]
 => 101100 => 44
[[.,[.,.]],.]
 => [1,1,0,0,1,0]
 => 110010 => 50
[[[.,.],.],.]
 => [1,0,1,0,1,0]
 => 101010 => 42
[.,[.,[.,[.,.]]]]
 => [1,1,1,1,0,0,0,0]
 => 11110000 => 240
[.,[.,[[.,.],.]]]
 => [1,1,1,0,1,0,0,0]
 => 11101000 => 232
[.,[[.,.],[.,.]]]
 => [1,1,0,1,1,0,0,0]
 => 11011000 => 216
[.,[[.,[.,.]],.]]
 => [1,1,1,0,0,1,0,0]
 => 11100100 => 228
[.,[[[.,.],.],.]]
 => [1,1,0,1,0,1,0,0]
 => 11010100 => 212
[[.,.],[.,[.,.]]]
 => [1,0,1,1,1,0,0,0]
 => 10111000 => 184
[[.,.],[[.,.],.]]
 => [1,0,1,1,0,1,0,0]
 => 10110100 => 180
[[.,[.,.]],[.,.]]
 => [1,1,0,0,1,1,0,0]
 => 11001100 => 204
[[[.,.],.],[.,.]]
 => [1,0,1,0,1,1,0,0]
 => 10101100 => 172
[[.,[.,[.,.]]],.]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => 226
[[.,[[.,.],.]],.]
 => [1,1,0,1,0,0,1,0]
 => 11010010 => 210
[[[.,.],[.,.]],.]
 => [1,0,1,1,0,0,1,0]
 => 10110010 => 178
[[[.,[.,.]],.],.]
 => [1,1,0,0,1,0,1,0]
 => 11001010 => 202
[[[[.,.],.],.],.]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 170
Description
The decimal representation of a binary word.