Riffs & Rotes

[Jon Awbrey]

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R&R.  Note 2

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SeqFans,

I have just submitted the following sequence:

A107532 [pending]

1  ,
1  1  ,
1  2  1  ,
1  3  1  1  ,
1  1  1  4  1  ,
1  5  2  9  1  1  ,
1  6  1  1  1  2  1  ,
1  7  1 25  1  3  1  1  ,
1  1  1 36  1  2  1  8  1  ,

Functional composition table for "n o m" = "n composed with m",
where n and m are the "primal codes" of finite partial functions
on the positive integers and 1 is the code for the empty function.

` ` ` ` ` ` ` ` ` ` `n o m
` ` ` ` ` ` ` ` ` ` ` \ /
` ` ` ` ` ` ` ` ` ` `1 . 1
` ` ` ` ` ` ` ` ` ` \ / \ /
` ` ` ` ` ` ` ` ` `2 . 1 . 2
` ` ` ` ` ` ` ` ` \ / \ / \ /
` ` ` ` ` ` ` ` `3 . 1 . 1 . 3
` ` ` ` ` ` ` ` \ / \ / \ / \ /
` ` ` ` ` ` ` `4 . 1 . 2 . 1 . 4
` ` ` ` ` ` ` \ / \ / \ / \ / \ /
` ` ` ` ` ` `5 . 1 . 3 . 1 . 1 . 5
` ` ` ` ` ` \ / \ / \ / \ / \ / \ /
` ` ` ` ` `6 . 1 . 1 . 1 . 4 . 1 . 6
` ` ` ` ` \ / \ / \ / \ / \ / \ / \ /
` ` ` ` `7 . 1 . 5 . 2 . 9 . 1 . 1 . 7
` ` ` ` \ / \ / \ / \ / \ / \ / \ / \ /
` ` ` `8 . 1 . 6 . 1 . 1 . 1 . 2 . 1 . 8
` ` ` \ / \ / \ / \ / \ / \ / \ / \ / \ /
` ` `9 . 1 . 7 . 1 . 25. 1 . 3 . 1 . 1 . 9
` ` \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
` 10 . 1 . 1 . 1 . 36. 1 . 2 . 1 . 8 . 1 . 10

Primal codes of finite partial functions on positive integers:

 1 = { }
 2 = 1:1
 3 = 2:1
 4 = 1:2
 5 = 3:1
 6 = 1:1 2:1
 7 = 4:1
 8 = 1:3
 9 = 2:2
10 = 1:1 3:1
11 = 5:1
12 = 1:2 2:1
13 = 6:1
14 = 1:1 4:1
15 = 2:1 3:1
16 = 1:4
17 = 7:1
18 = 1:1 2:2
19 = 8:1
20 = 1:2 3:1

Cf. A061396, A062504, A062537, A062860

Jon Awbrey

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