Riffs & Rotes

[Jon Awbrey]

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R&R.  Note 1

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Neil, SeqFans,

I just realized that the "line of identity" trick that I borrowed from
C.S. Peirce would allow me to draw the "rotes" of non-negative integers
in a much more regular fashion, as I draw the first score of them below.

Rotes ("rooted odd trees with only exponent symmetries") for the
non-negative integers from 1 to 20.  The root node is indicated
by a subtended caret (^), and figures like "o===o" represent
identified nodes.  Each number may be taken as the code of
a finite function whose domain and range are finite sets
of previously constructed numbers, represented below as
finite sets of ordered pairs.

Cf. http://www.research.att.com/projects/OEIS?Anum=A061396
Cf. http://www.research.att.com/~njas/sequences/a061396a.txt

o
^
1 = 0:0

o-o
|
o
^
2 = 1:1

o-o
|
o-o
|
o
^
3 = 2:1

  o-o
  |
o-o
|
o
^
4 = 1:2

o-o
|
o-o
|
o-o
|
o
^
5 = 3:1

    o-o
    |
o-o o-o
|   |
o===o
^
6 = 1:1 2:1

  o-o
  |
o-o
|
o-o
|
o
^
7 = 4:1

  o-o
  |
  o-o
  |
o-o
|
o
^
8 = 1:3

o-o o-o
|   |
o---o
|
o
^
9 = 2:2

    o-o
    |
    o-o
    |
o-o o-o
|   |
o===o
^
10 = 1:1 3:1

o-o
|
o-o
|
o-o
|
o-o
|
o
^
11 = 5:1

  o-o o-o
  |   |
o-o   o-o
|     |
o=====o
^
12 = 1:2 2:1

    o-o
    |
o-o o-o
|   |
o===o-o
|
o
^
13 = 6:1

      o-o
      |
    o-o
    |
o-o o-o
|   |
o===o
^
14 = 1:1 4:1

    o-o
    |
o-o o-o
|   |
o-o o-o
|   |
o===o
^
15 = 2:1 3:1

    o-o
    |
  o-o
  |
o-o
|
o
^
16 = 1:4

  o-o
  |
o-o
|
o-o
|
o-o
|
o
^
17 = 7:1

    o-o o-o
    |   |
o-o o---o
|   |
o===o
^
18 = 1:1 2:2

  o-o
  |
  o-o
  |
o-o
|
o-o
|
o
^
19 = 8:1

      o-o
      |
  o-o o-o
  |   |
o-o   o-o
|     |
o=====o
^
20 = 1:2 3:1

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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