Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Inactive » math-history-list

Topic: Fibonacci, compositions, history
Replies: 6   Last Post: Feb 21, 2012 10:22 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Brian Hopkins

Posts: 9
Registered: 12/4/04
Fibonacci, compositions, history
Posted: Mar 27, 2011 1:48 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

There are three basic families of restricted compositions (ordered partitions) that are enumerated by the Fibonacci numbers (with offsets):

a) compositions with parts from {1,2}
(e.g., 2+2 = 2+1+1 = 1+2+1 = 1+1+2 = 1+1+1+1)

b) compositions that do not have 1 as a part
(e.g., 6 = 4+2 = 3+3 = 2+4 = 2+2+2)

c) compositions that only have odd parts
(e.g., 5 = 3+1+1 = 1+3+1 = 1+1+3 = 1+1+1+1+1)

The connection between (a) & the Fibonacci numbers traces back to the analysis of Vedic poetry in the first millennium C.E., at least (Singh, Hist. Math. 12, 1985). I believe Cayley is responsible for the connection to (b). Who first established the connection with (c), odd-part compositions? It was known by the early years of the Fibonacci Quarterly (1960s), but I suspect it was done before that. Thanks for any assistance, especially with citations. --Brian Hopkins



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.