Identifier
- St000396: Binary trees ⟶ ℤ
Values
=>
Cc0010;cc-rep
[.,.]=>1
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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
[[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>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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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.
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)
Created
Feb 22, 2016 at 08:21 by Martin Rubey
Updated
Feb 22, 2016 at 08:57 by Martin Rubey
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