Jon Awbrey
2014-07-31 14:15:50 UTC
Re: Dana Scott
At: http://www.cs.nyu.edu/pipermail/fom/2014-July/018046.html
Re: Tim Chow
At: http://www.cs.nyu.edu/pipermail/fom/2014-July/018053.html
I can't remember when I first started playing with Gödel codings of graph-theoretic structures,
which arose in logical and computational settings, but I remember being egged on in that direction
by Martin Gardner's 1976 column on Catalan numbers, planted plane trees, polygon dissections, etc.
Codings being injections from a combinatorial species S to integers, either non-negatives N or
positives M, I was especially interested in codings that were also surjective, thereby revealing
something about the target domain of arithmetic.
The most interesting bijection I found was between positive integers M and finite partial functions
from M to M. All of this comes straight out of the primes factorizations. That type of bijection
may remind some people of Dana Scott's D_∞. Corresponding to the positive integers there arose two
species of graphical structures, which I dubbed "riffs" and "rotes". See these links for more info:
https://oeis.org/wiki/Riffs_and_Rotes
http://oeis.org/A061396
http://oeis.org/A111788
Jon
http://inquiryintoinquiry.com/
http://www.oeis.org/wiki/User:Jon_Awbrey
At: http://www.cs.nyu.edu/pipermail/fom/2014-July/018046.html
Re: Tim Chow
At: http://www.cs.nyu.edu/pipermail/fom/2014-July/018053.html
I can't remember when I first started playing with Gödel codings of graph-theoretic structures,
which arose in logical and computational settings, but I remember being egged on in that direction
by Martin Gardner's 1976 column on Catalan numbers, planted plane trees, polygon dissections, etc.
Codings being injections from a combinatorial species S to integers, either non-negatives N or
positives M, I was especially interested in codings that were also surjective, thereby revealing
something about the target domain of arithmetic.
The most interesting bijection I found was between positive integers M and finite partial functions
from M to M. All of this comes straight out of the primes factorizations. That type of bijection
may remind some people of Dana Scott's D_∞. Corresponding to the positive integers there arose two
species of graphical structures, which I dubbed "riffs" and "rotes". See these links for more info:
https://oeis.org/wiki/Riffs_and_Rotes
http://oeis.org/A061396
http://oeis.org/A111788
Jon
http://inquiryintoinquiry.com/
http://www.oeis.org/wiki/User:Jon_Awbrey