Re: Riffs and Rotes

Post       : Riffs and Rotes : 2
URL        : http://inquiryintoinquiry.com/2013/03/03/riffs-and-rotes-2/
Posted     : March 3, 2013 at 10:24 am
Author     : Jon Awbrey
Categories : Algebra, Combinatorics, Graph Theory, Group Theory,
              Mathematics, Number Theory, Riffs and Rotes

Re: Peter Cameron
At: http://cameroncounts.wordpress.com/2013/03/03/two-lectures/

The interaction between addition and multiplication on the natural numbers
has long been an interest of mine, leading to broader questions about the
relationship between algebra and combinatorics.  My gropings with these
enigmas led me to the structures of Riffs and Rotes [1], extracting
what we might think of as the “purely combinatorial” properties of
primes factorizations.  Thinking of the additive structure of the
positive integers as embodied in their linear ordering, the first
couple of questions that arise here are these —

• How much of the natural ordering of the natural numbers is purely combinatorial?
• What extra axioms on the partial orders of Riffs and Rotes would restore their natural order?

--

[1] http://inquiryintoinquiry.com/2013/01/28/riffs-and-rotes-1/

-- 

academia: http://independent.academia.edu/JonAwbrey
my word press blog: http://inquiryintoinquiry.com/
inquiry list: http://stderr.org/pipermail/inquiry/
mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey
oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey
facebook page: https://www.facebook.com/JonnyCache