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* www.FindStat.org - The Combinatorial Statistic Finder *
* *
* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* This information is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
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-----------------------------------------------------------------------------
Statistic identifier: St000396
-----------------------------------------------------------------------------
Collection: Binary trees
-----------------------------------------------------------------------------
Description: The register function (or Horton-Strahler number) of a binary tree.
This is different from the dimension of the associated poset for the tree $[[[.,.],[.,.]],[[.,.],[.,.]]]$: its register function is 3, whereas the dimension of the associated poset is 2.
-----------------------------------------------------------------------------
References: [1] Hackl, B., Heuberger, C., Prodinger, H. The Register Function and Reductions of Binary Trees and Lattice Paths [[arXiv:1602.06200]]
-----------------------------------------------------------------------------
Code:
def statistic(B):
if B.is_empty():
return 0
else:
r1 = statistic(B[0])
r2 = statistic(B[1])
if r1 == r2:
return r1+1
else:
return max(r1, r2)
-----------------------------------------------------------------------------
Statistic values:
[.,.] => 1
[.,[.,.]] => 1
[[.,.],.] => 1
[.,[.,[.,.]]] => 1
[.,[[.,.],.]] => 1
[[.,.],[.,.]] => 2
[[.,[.,.]],.] => 1
[[[.,.],.],.] => 1
[.,[.,[.,[.,.]]]] => 1
[.,[.,[[.,.],.]]] => 1
[.,[[.,.],[.,.]]] => 2
[.,[[.,[.,.]],.]] => 1
[.,[[[.,.],.],.]] => 1
[[.,.],[.,[.,.]]] => 2
[[.,.],[[.,.],.]] => 2
[[.,[.,.]],[.,.]] => 2
[[[.,.],.],[.,.]] => 2
[[.,[.,[.,.]]],.] => 1
[[.,[[.,.],.]],.] => 1
[[[.,.],[.,.]],.] => 2
[[[.,[.,.]],.],.] => 1
[[[[.,.],.],.],.] => 1
[.,[.,[.,[.,[.,.]]]]] => 1
[.,[.,[.,[[.,.],.]]]] => 1
[.,[.,[[.,.],[.,.]]]] => 2
[.,[.,[[.,[.,.]],.]]] => 1
[.,[.,[[[.,.],.],.]]] => 1
[.,[[.,.],[.,[.,.]]]] => 2
[.,[[.,.],[[.,.],.]]] => 2
[.,[[.,[.,.]],[.,.]]] => 2
[.,[[[.,.],.],[.,.]]] => 2
[.,[[.,[.,[.,.]]],.]] => 1
[.,[[.,[[.,.],.]],.]] => 1
[.,[[[.,.],[.,.]],.]] => 2
[.,[[[.,[.,.]],.],.]] => 1
[.,[[[[.,.],.],.],.]] => 1
[[.,.],[.,[.,[.,.]]]] => 2
[[.,.],[.,[[.,.],.]]] => 2
[[.,.],[[.,.],[.,.]]] => 2
[[.,.],[[.,[.,.]],.]] => 2
[[.,.],[[[.,.],.],.]] => 2
[[.,[.,.]],[.,[.,.]]] => 2
[[.,[.,.]],[[.,.],.]] => 2
[[[.,.],.],[.,[.,.]]] => 2
[[[.,.],.],[[.,.],.]] => 2
[[.,[.,[.,.]]],[.,.]] => 2
[[.,[[.,.],.]],[.,.]] => 2
[[[.,.],[.,.]],[.,.]] => 2
[[[.,[.,.]],.],[.,.]] => 2
[[[[.,.],.],.],[.,.]] => 2
[[.,[.,[.,[.,.]]]],.] => 1
[[.,[.,[[.,.],.]]],.] => 1
[[.,[[.,.],[.,.]]],.] => 2
[[.,[[.,[.,.]],.]],.] => 1
[[.,[[[.,.],.],.]],.] => 1
[[[.,.],[.,[.,.]]],.] => 2
[[[.,.],[[.,.],.]],.] => 2
[[[.,[.,.]],[.,.]],.] => 2
[[[[.,.],.],[.,.]],.] => 2
[[[.,[.,[.,.]]],.],.] => 1
[[[.,[[.,.],.]],.],.] => 1
[[[[.,.],[.,.]],.],.] => 2
[[[[.,[.,.]],.],.],.] => 1
[[[[[.,.],.],.],.],.] => 1
[.,[.,[.,[.,[.,[.,.]]]]]] => 1
[.,[.,[.,[.,[[.,.],.]]]]] => 1
[.,[.,[.,[[.,.],[.,.]]]]] => 2
[.,[.,[.,[[.,[.,.]],.]]]] => 1
[.,[.,[.,[[[.,.],.],.]]]] => 1
[.,[.,[[.,.],[.,[.,.]]]]] => 2
[.,[.,[[.,.],[[.,.],.]]]] => 2
[.,[.,[[.,[.,.]],[.,.]]]] => 2
[.,[.,[[[.,.],.],[.,.]]]] => 2
[.,[.,[[.,[.,[.,.]]],.]]] => 1
[.,[.,[[.,[[.,.],.]],.]]] => 1
[.,[.,[[[.,.],[.,.]],.]]] => 2
[.,[.,[[[.,[.,.]],.],.]]] => 1
[.,[.,[[[[.,.],.],.],.]]] => 1
[.,[[.,.],[.,[.,[.,.]]]]] => 2
[.,[[.,.],[.,[[.,.],.]]]] => 2
[.,[[.,.],[[.,.],[.,.]]]] => 2
[.,[[.,.],[[.,[.,.]],.]]] => 2
[.,[[.,.],[[[.,.],.],.]]] => 2
[.,[[.,[.,.]],[.,[.,.]]]] => 2
[.,[[.,[.,.]],[[.,.],.]]] => 2
[.,[[[.,.],.],[.,[.,.]]]] => 2
[.,[[[.,.],.],[[.,.],.]]] => 2
[.,[[.,[.,[.,.]]],[.,.]]] => 2
[.,[[.,[[.,.],.]],[.,.]]] => 2
[.,[[[.,.],[.,.]],[.,.]]] => 2
[.,[[[.,[.,.]],.],[.,.]]] => 2
[.,[[[[.,.],.],.],[.,.]]] => 2
[.,[[.,[.,[.,[.,.]]]],.]] => 1
[.,[[.,[.,[[.,.],.]]],.]] => 1
[.,[[.,[[.,.],[.,.]]],.]] => 2
[.,[[.,[[.,[.,.]],.]],.]] => 1
[.,[[.,[[[.,.],.],.]],.]] => 1
[.,[[[.,.],[.,[.,.]]],.]] => 2
[.,[[[.,.],[[.,.],.]],.]] => 2
[.,[[[.,[.,.]],[.,.]],.]] => 2
[.,[[[[.,.],.],[.,.]],.]] => 2
[.,[[[.,[.,[.,.]]],.],.]] => 1
[.,[[[.,[[.,.],.]],.],.]] => 1
[.,[[[[.,.],[.,.]],.],.]] => 2
[.,[[[[.,[.,.]],.],.],.]] => 1
[.,[[[[[.,.],.],.],.],.]] => 1
[[.,.],[.,[.,[.,[.,.]]]]] => 2
[[.,.],[.,[.,[[.,.],.]]]] => 2
[[.,.],[.,[[.,.],[.,.]]]] => 2
[[.,.],[.,[[.,[.,.]],.]]] => 2
[[.,.],[.,[[[.,.],.],.]]] => 2
[[.,.],[[.,.],[.,[.,.]]]] => 2
[[.,.],[[.,.],[[.,.],.]]] => 2
[[.,.],[[.,[.,.]],[.,.]]] => 2
[[.,.],[[[.,.],.],[.,.]]] => 2
[[.,.],[[.,[.,[.,.]]],.]] => 2
[[.,.],[[.,[[.,.],.]],.]] => 2
[[.,.],[[[.,.],[.,.]],.]] => 2
[[.,.],[[[.,[.,.]],.],.]] => 2
[[.,.],[[[[.,.],.],.],.]] => 2
[[.,[.,.]],[.,[.,[.,.]]]] => 2
[[.,[.,.]],[.,[[.,.],.]]] => 2
[[.,[.,.]],[[.,.],[.,.]]] => 2
[[.,[.,.]],[[.,[.,.]],.]] => 2
[[.,[.,.]],[[[.,.],.],.]] => 2
[[[.,.],.],[.,[.,[.,.]]]] => 2
[[[.,.],.],[.,[[.,.],.]]] => 2
[[[.,.],.],[[.,.],[.,.]]] => 2
[[[.,.],.],[[.,[.,.]],.]] => 2
[[[.,.],.],[[[.,.],.],.]] => 2
[[.,[.,[.,.]]],[.,[.,.]]] => 2
[[.,[.,[.,.]]],[[.,.],.]] => 2
[[.,[[.,.],.]],[.,[.,.]]] => 2
[[.,[[.,.],.]],[[.,.],.]] => 2
[[[.,.],[.,.]],[.,[.,.]]] => 2
[[[.,.],[.,.]],[[.,.],.]] => 2
[[[.,[.,.]],.],[.,[.,.]]] => 2
[[[.,[.,.]],.],[[.,.],.]] => 2
[[[[.,.],.],.],[.,[.,.]]] => 2
[[[[.,.],.],.],[[.,.],.]] => 2
[[.,[.,[.,[.,.]]]],[.,.]] => 2
[[.,[.,[[.,.],.]]],[.,.]] => 2
[[.,[[.,.],[.,.]]],[.,.]] => 2
[[.,[[.,[.,.]],.]],[.,.]] => 2
[[.,[[[.,.],.],.]],[.,.]] => 2
[[[.,.],[.,[.,.]]],[.,.]] => 2
[[[.,.],[[.,.],.]],[.,.]] => 2
[[[.,[.,.]],[.,.]],[.,.]] => 2
[[[[.,.],.],[.,.]],[.,.]] => 2
[[[.,[.,[.,.]]],.],[.,.]] => 2
[[[.,[[.,.],.]],.],[.,.]] => 2
[[[[.,.],[.,.]],.],[.,.]] => 2
[[[[.,[.,.]],.],.],[.,.]] => 2
[[[[[.,.],.],.],.],[.,.]] => 2
[[.,[.,[.,[.,[.,.]]]]],.] => 1
[[.,[.,[.,[[.,.],.]]]],.] => 1
[[.,[.,[[.,.],[.,.]]]],.] => 2
[[.,[.,[[.,[.,.]],.]]],.] => 1
[[.,[.,[[[.,.],.],.]]],.] => 1
[[.,[[.,.],[.,[.,.]]]],.] => 2
[[.,[[.,.],[[.,.],.]]],.] => 2
[[.,[[.,[.,.]],[.,.]]],.] => 2
[[.,[[[.,.],.],[.,.]]],.] => 2
[[.,[[.,[.,[.,.]]],.]],.] => 1
[[.,[[.,[[.,.],.]],.]],.] => 1
[[.,[[[.,.],[.,.]],.]],.] => 2
[[.,[[[.,[.,.]],.],.]],.] => 1
[[.,[[[[.,.],.],.],.]],.] => 1
[[[.,.],[.,[.,[.,.]]]],.] => 2
[[[.,.],[.,[[.,.],.]]],.] => 2
[[[.,.],[[.,.],[.,.]]],.] => 2
[[[.,.],[[.,[.,.]],.]],.] => 2
[[[.,.],[[[.,.],.],.]],.] => 2
[[[.,[.,.]],[.,[.,.]]],.] => 2
[[[.,[.,.]],[[.,.],.]],.] => 2
[[[[.,.],.],[.,[.,.]]],.] => 2
[[[[.,.],.],[[.,.],.]],.] => 2
[[[.,[.,[.,.]]],[.,.]],.] => 2
[[[.,[[.,.],.]],[.,.]],.] => 2
[[[[.,.],[.,.]],[.,.]],.] => 2
[[[[.,[.,.]],.],[.,.]],.] => 2
[[[[[.,.],.],.],[.,.]],.] => 2
[[[.,[.,[.,[.,.]]]],.],.] => 1
[[[.,[.,[[.,.],.]]],.],.] => 1
[[[.,[[.,.],[.,.]]],.],.] => 2
[[[.,[[.,[.,.]],.]],.],.] => 1
[[[.,[[[.,.],.],.]],.],.] => 1
[[[[.,.],[.,[.,.]]],.],.] => 2
[[[[.,.],[[.,.],.]],.],.] => 2
[[[[.,[.,.]],[.,.]],.],.] => 2
[[[[[.,.],.],[.,.]],.],.] => 2
[[[[.,[.,[.,.]]],.],.],.] => 1
[[[[.,[[.,.],.]],.],.],.] => 1
[[[[[.,.],[.,.]],.],.],.] => 2
[[[[[.,[.,.]],.],.],.],.] => 1
[[[[[[.,.],.],.],.],.],.] => 1
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => 1
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => 1
[.,[.,[.,[.,[[[.,.],.],.]]]]] => 1
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[.,[.,[.,[[.,.],[[.,.],.]]]]] => 2
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[.,[.,[.,[[[.,.],.],[.,.]]]]] => 2
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => 1
[.,[.,[.,[[.,[[.,.],.]],.]]]] => 1
[.,[.,[.,[[[.,.],[.,.]],.]]]] => 2
[.,[.,[.,[[[.,[.,.]],.],.]]]] => 1
[.,[.,[.,[[[[.,.],.],.],.]]]] => 1
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[.,[.,[[.,.],[.,[[.,.],.]]]]] => 2
[.,[.,[[.,.],[[.,.],[.,.]]]]] => 2
[.,[.,[[.,.],[[.,[.,.]],.]]]] => 2
[.,[.,[[.,.],[[[.,.],.],.]]]] => 2
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[.,[.,[[.,[.,.]],[[.,.],.]]]] => 2
[.,[.,[[[.,.],.],[.,[.,.]]]]] => 2
[.,[.,[[[.,.],.],[[.,.],.]]]] => 2
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[.,[.,[[.,[[.,.],.]],[.,.]]]] => 2
[.,[.,[[[.,.],[.,.]],[.,.]]]] => 2
[.,[.,[[[.,[.,.]],.],[.,.]]]] => 2
[.,[.,[[[[.,.],.],.],[.,.]]]] => 2
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => 1
[.,[.,[[.,[.,[[.,.],.]]],.]]] => 1
[.,[.,[[.,[[.,.],[.,.]]],.]]] => 2
[.,[.,[[.,[[.,[.,.]],.]],.]]] => 1
[.,[.,[[.,[[[.,.],.],.]],.]]] => 1
[.,[.,[[[.,.],[.,[.,.]]],.]]] => 2
[.,[.,[[[.,.],[[.,.],.]],.]]] => 2
[.,[.,[[[.,[.,.]],[.,.]],.]]] => 2
[.,[.,[[[[.,.],.],[.,.]],.]]] => 2
[.,[.,[[[.,[.,[.,.]]],.],.]]] => 1
[.,[.,[[[.,[[.,.],.]],.],.]]] => 1
[.,[.,[[[[.,.],[.,.]],.],.]]] => 2
[.,[.,[[[[.,[.,.]],.],.],.]]] => 1
[.,[.,[[[[[.,.],.],.],.],.]]] => 1
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[.,[[.,.],[.,[.,[[.,.],.]]]]] => 2
[.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[.,[[.,.],[.,[[.,[.,.]],.]]]] => 2
[.,[[.,.],[.,[[[.,.],.],.]]]] => 2
[.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[.,[[.,.],[[.,.],[[.,.],.]]]] => 2
[.,[[.,.],[[.,[.,.]],[.,.]]]] => 2
[.,[[.,.],[[[.,.],.],[.,.]]]] => 2
[.,[[.,.],[[.,[.,[.,.]]],.]]] => 2
[.,[[.,.],[[.,[[.,.],.]],.]]] => 2
[.,[[.,.],[[[.,.],[.,.]],.]]] => 2
[.,[[.,.],[[[.,[.,.]],.],.]]] => 2
[.,[[.,.],[[[[.,.],.],.],.]]] => 2
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[.,[[.,[.,.]],[.,[[.,.],.]]]] => 2
[.,[[.,[.,.]],[[.,.],[.,.]]]] => 2
[.,[[.,[.,.]],[[.,[.,.]],.]]] => 2
[.,[[.,[.,.]],[[[.,.],.],.]]] => 2
[.,[[[.,.],.],[.,[.,[.,.]]]]] => 2
[.,[[[.,.],.],[.,[[.,.],.]]]] => 2
[.,[[[.,.],.],[[.,.],[.,.]]]] => 2
[.,[[[.,.],.],[[.,[.,.]],.]]] => 2
[.,[[[.,.],.],[[[.,.],.],.]]] => 2
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[.,[[.,[.,[.,.]]],[[.,.],.]]] => 2
[.,[[.,[[.,.],.]],[.,[.,.]]]] => 2
[.,[[.,[[.,.],.]],[[.,.],.]]] => 2
[.,[[[.,.],[.,.]],[.,[.,.]]]] => 2
[.,[[[.,.],[.,.]],[[.,.],.]]] => 2
[.,[[[.,[.,.]],.],[.,[.,.]]]] => 2
[.,[[[.,[.,.]],.],[[.,.],.]]] => 2
[.,[[[[.,.],.],.],[.,[.,.]]]] => 2
[.,[[[[.,.],.],.],[[.,.],.]]] => 2
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[.,[[.,[.,[[.,.],.]]],[.,.]]] => 2
[.,[[.,[[.,.],[.,.]]],[.,.]]] => 2
[.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[.,[[.,[[[.,.],.],.]],[.,.]]] => 2
[.,[[[.,.],[.,[.,.]]],[.,.]]] => 2
[.,[[[.,.],[[.,.],.]],[.,.]]] => 2
[.,[[[.,[.,.]],[.,.]],[.,.]]] => 2
[.,[[[[.,.],.],[.,.]],[.,.]]] => 2
[.,[[[.,[.,[.,.]]],.],[.,.]]] => 2
[.,[[[.,[[.,.],.]],.],[.,.]]] => 2
[.,[[[[.,.],[.,.]],.],[.,.]]] => 2
[.,[[[[.,[.,.]],.],.],[.,.]]] => 2
[.,[[[[[.,.],.],.],.],[.,.]]] => 2
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => 1
[.,[[.,[.,[.,[[.,.],.]]]],.]] => 1
[.,[[.,[.,[[.,.],[.,.]]]],.]] => 2
[.,[[.,[.,[[.,[.,.]],.]]],.]] => 1
[.,[[.,[.,[[[.,.],.],.]]],.]] => 1
[.,[[.,[[.,.],[.,[.,.]]]],.]] => 2
[.,[[.,[[.,.],[[.,.],.]]],.]] => 2
[.,[[.,[[.,[.,.]],[.,.]]],.]] => 2
[.,[[.,[[[.,.],.],[.,.]]],.]] => 2
[.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[.,[[.,[[.,[[.,.],.]],.]],.]] => 1
[.,[[.,[[[.,.],[.,.]],.]],.]] => 2
[.,[[.,[[[.,[.,.]],.],.]],.]] => 1
[.,[[.,[[[[.,.],.],.],.]],.]] => 1
[.,[[[.,.],[.,[.,[.,.]]]],.]] => 2
[.,[[[.,.],[.,[[.,.],.]]],.]] => 2
[.,[[[.,.],[[.,.],[.,.]]],.]] => 2
[.,[[[.,.],[[.,[.,.]],.]],.]] => 2
[.,[[[.,.],[[[.,.],.],.]],.]] => 2
[.,[[[.,[.,.]],[.,[.,.]]],.]] => 2
[.,[[[.,[.,.]],[[.,.],.]],.]] => 2
[.,[[[[.,.],.],[.,[.,.]]],.]] => 2
[.,[[[[.,.],.],[[.,.],.]],.]] => 2
[.,[[[.,[.,[.,.]]],[.,.]],.]] => 2
[.,[[[.,[[.,.],.]],[.,.]],.]] => 2
[.,[[[[.,.],[.,.]],[.,.]],.]] => 2
[.,[[[[.,[.,.]],.],[.,.]],.]] => 2
[.,[[[[[.,.],.],.],[.,.]],.]] => 2
[.,[[[.,[.,[.,[.,.]]]],.],.]] => 1
[.,[[[.,[.,[[.,.],.]]],.],.]] => 1
[.,[[[.,[[.,.],[.,.]]],.],.]] => 2
[.,[[[.,[[.,[.,.]],.]],.],.]] => 1
[.,[[[.,[[[.,.],.],.]],.],.]] => 1
[.,[[[[.,.],[.,[.,.]]],.],.]] => 2
[.,[[[[.,.],[[.,.],.]],.],.]] => 2
[.,[[[[.,[.,.]],[.,.]],.],.]] => 2
[.,[[[[[.,.],.],[.,.]],.],.]] => 2
[.,[[[[.,[.,[.,.]]],.],.],.]] => 1
[.,[[[[.,[[.,.],.]],.],.],.]] => 1
[.,[[[[[.,.],[.,.]],.],.],.]] => 2
[.,[[[[[.,[.,.]],.],.],.],.]] => 1
[.,[[[[[[.,.],.],.],.],.],.]] => 1
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => 2
[[.,.],[.,[.,[.,[[.,.],.]]]]] => 2
[[.,.],[.,[.,[[.,.],[.,.]]]]] => 2
[[.,.],[.,[.,[[.,[.,.]],.]]]] => 2
[[.,.],[.,[.,[[[.,.],.],.]]]] => 2
[[.,.],[.,[[.,.],[.,[.,.]]]]] => 2
[[.,.],[.,[[.,.],[[.,.],.]]]] => 2
[[.,.],[.,[[.,[.,.]],[.,.]]]] => 2
[[.,.],[.,[[[.,.],.],[.,.]]]] => 2
[[.,.],[.,[[.,[.,[.,.]]],.]]] => 2
[[.,.],[.,[[.,[[.,.],.]],.]]] => 2
[[.,.],[.,[[[.,.],[.,.]],.]]] => 2
[[.,.],[.,[[[.,[.,.]],.],.]]] => 2
[[.,.],[.,[[[[.,.],.],.],.]]] => 2
[[.,.],[[.,.],[.,[.,[.,.]]]]] => 2
[[.,.],[[.,.],[.,[[.,.],.]]]] => 2
[[.,.],[[.,.],[[.,.],[.,.]]]] => 2
[[.,.],[[.,.],[[.,[.,.]],.]]] => 2
[[.,.],[[.,.],[[[.,.],.],.]]] => 2
[[.,.],[[.,[.,.]],[.,[.,.]]]] => 2
[[.,.],[[.,[.,.]],[[.,.],.]]] => 2
[[.,.],[[[.,.],.],[.,[.,.]]]] => 2
[[.,.],[[[.,.],.],[[.,.],.]]] => 2
[[.,.],[[.,[.,[.,.]]],[.,.]]] => 2
[[.,.],[[.,[[.,.],.]],[.,.]]] => 2
[[.,.],[[[.,.],[.,.]],[.,.]]] => 2
[[.,.],[[[.,[.,.]],.],[.,.]]] => 2
[[.,.],[[[[.,.],.],.],[.,.]]] => 2
[[.,.],[[.,[.,[.,[.,.]]]],.]] => 2
[[.,.],[[.,[.,[[.,.],.]]],.]] => 2
[[.,.],[[.,[[.,.],[.,.]]],.]] => 2
[[.,.],[[.,[[.,[.,.]],.]],.]] => 2
[[.,.],[[.,[[[.,.],.],.]],.]] => 2
[[.,.],[[[.,.],[.,[.,.]]],.]] => 2
[[.,.],[[[.,.],[[.,.],.]],.]] => 2
[[.,.],[[[.,[.,.]],[.,.]],.]] => 2
[[.,.],[[[[.,.],.],[.,.]],.]] => 2
[[.,.],[[[.,[.,[.,.]]],.],.]] => 2
[[.,.],[[[.,[[.,.],.]],.],.]] => 2
[[.,.],[[[[.,.],[.,.]],.],.]] => 2
[[.,.],[[[[.,[.,.]],.],.],.]] => 2
[[.,.],[[[[[.,.],.],.],.],.]] => 2
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => 2
[[.,[.,.]],[.,[.,[[.,.],.]]]] => 2
[[.,[.,.]],[.,[[.,.],[.,.]]]] => 2
[[.,[.,.]],[.,[[.,[.,.]],.]]] => 2
[[.,[.,.]],[.,[[[.,.],.],.]]] => 2
[[.,[.,.]],[[.,.],[.,[.,.]]]] => 2
[[.,[.,.]],[[.,.],[[.,.],.]]] => 2
[[.,[.,.]],[[.,[.,.]],[.,.]]] => 2
[[.,[.,.]],[[[.,.],.],[.,.]]] => 2
[[.,[.,.]],[[.,[.,[.,.]]],.]] => 2
[[.,[.,.]],[[.,[[.,.],.]],.]] => 2
[[.,[.,.]],[[[.,.],[.,.]],.]] => 2
[[.,[.,.]],[[[.,[.,.]],.],.]] => 2
[[.,[.,.]],[[[[.,.],.],.],.]] => 2
[[[.,.],.],[.,[.,[.,[.,.]]]]] => 2
[[[.,.],.],[.,[.,[[.,.],.]]]] => 2
[[[.,.],.],[.,[[.,.],[.,.]]]] => 2
[[[.,.],.],[.,[[.,[.,.]],.]]] => 2
[[[.,.],.],[.,[[[.,.],.],.]]] => 2
[[[.,.],.],[[.,.],[.,[.,.]]]] => 2
[[[.,.],.],[[.,.],[[.,.],.]]] => 2
[[[.,.],.],[[.,[.,.]],[.,.]]] => 2
[[[.,.],.],[[[.,.],.],[.,.]]] => 2
[[[.,.],.],[[.,[.,[.,.]]],.]] => 2
[[[.,.],.],[[.,[[.,.],.]],.]] => 2
[[[.,.],.],[[[.,.],[.,.]],.]] => 2
[[[.,.],.],[[[.,[.,.]],.],.]] => 2
[[[.,.],.],[[[[.,.],.],.],.]] => 2
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => 2
[[.,[.,[.,.]]],[.,[[.,.],.]]] => 2
[[.,[.,[.,.]]],[[.,.],[.,.]]] => 2
[[.,[.,[.,.]]],[[.,[.,.]],.]] => 2
[[.,[.,[.,.]]],[[[.,.],.],.]] => 2
[[.,[[.,.],.]],[.,[.,[.,.]]]] => 2
[[.,[[.,.],.]],[.,[[.,.],.]]] => 2
[[.,[[.,.],.]],[[.,.],[.,.]]] => 2
[[.,[[.,.],.]],[[.,[.,.]],.]] => 2
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[[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => 2
[[.,.],[[.,[[[.,.],.],.]],[.,.]]] => 2
[[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => 2
[[.,.],[[[.,.],[[.,.],.]],[.,.]]] => 2
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => 2
[[.,.],[[[[.,.],.],[.,.]],[.,.]]] => 2
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[[.,.],[[.,[[[[.,.],.],.],.]],.]] => 2
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => 2
[[.,.],[[[.,.],[.,[[.,.],.]]],.]] => 2
[[.,.],[[[.,.],[[.,.],[.,.]]],.]] => 2
[[.,.],[[[.,.],[[.,[.,.]],.]],.]] => 2
[[.,.],[[[.,.],[[[.,.],.],.]],.]] => 2
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => 2
[[.,.],[[[.,[.,.]],[[.,.],.]],.]] => 2
[[.,.],[[[[.,.],.],[.,[.,.]]],.]] => 2
[[.,.],[[[[.,.],.],[[.,.],.]],.]] => 2
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => 2
[[.,.],[[[.,[[.,.],.]],[.,.]],.]] => 2
[[.,.],[[[[.,.],[.,.]],[.,.]],.]] => 2
[[.,.],[[[[.,[.,.]],.],[.,.]],.]] => 2
[[.,.],[[[[[.,.],.],.],[.,.]],.]] => 2
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => 2
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[[.,.],[[[.,[[.,.],[.,.]]],.],.]] => 2
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => 2
[[.,.],[[[.,[[[.,.],.],.]],.],.]] => 2
[[.,.],[[[[.,.],[.,[.,.]]],.],.]] => 2
[[.,.],[[[[.,.],[[.,.],.]],.],.]] => 2
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => 2
[[.,.],[[[[[.,.],.],[.,.]],.],.]] => 2
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => 2
[[.,.],[[[[.,[[.,.],.]],.],.],.]] => 2
[[.,.],[[[[[.,.],[.,.]],.],.],.]] => 2
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => 2
[[.,.],[[[[[[.,.],.],.],.],.],.]] => 2
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 2
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 2
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => 2
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => 2
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 2
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 2
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => 2
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => 2
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => 2
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => 2
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => 2
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => 2
-----------------------------------------------------------------------------
Created: Feb 22, 2016 at 08:21 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Feb 22, 2016 at 08:57 by Martin Rubey