Advances and Applications in Discrete Mathematics
Volume 2, Issue 2, Pages 85 - 95
(October 2008)
|
|
A MULTISET-VALUED FIBONACCI-TYPE SEQUENCE
Tamas Kalmar-Nagy (USA)
|
Abstract: We investigate the structure of a multiset-valued Fibonacci-type sequence created by set union/sum/difference operations. A closed-form generating function is derived to explicitly characterize the elements of these sets and their exact averages and variances. The geometric mean of the sets is numerically demonstrated to exponentially grow, and we prove that the exponent is the square root of the golden ratio. |
Keywords and phrases: Fibonacci sequence, generating function, multiset, Minkowski sum. |
|
Number of Downloads: 269 | Number of Views: 685 |
|