Colored Partitions and the Fibonacci Sequence
نویسندگان
چکیده
منابع مشابه
Fibonacci Partitions
Then f(z) is also an analytic function without zeros on compact subsets of the unit disk. We have A * ) = n o * * ) 1 = z v < °=0(4) «>1 «>0 Definition 1: Let r(#)? r^(n), r0(w) denote, respectively, the number of partitions of n into distinct parts, evenly many distinct parts, oddly many distinct parts from {un}. Let r (0) = rE(0) = l, r0(0) = 0. If an =rE(n)-rQ(n)9 then U„ is the number of pa...
متن کاملThe Fibonacci Sequence in Successive Partitions of a Golden Triangle
A Golden Triangle is a triangle with two of its sides in the ratio (J>:1, where is the Fibonacci Ratio, i.e., (J> = ^(1 + /J) ^ 1.618. Let AABC be a triangle whose sides are a,b, and o and let a/b = k > 1. Bicknell and Hoggatt [1] have shown that (1) a triangle with a side equal to b can be removed from AABC to leave a triangle similar to AABC if and only if k = cj), and (2) a triangle simi...
متن کاملGraphs, partitions and Fibonacci numbers
The Fibonacci number of a graph is the number of independent vertex subsets. In this paper, we investigate trees with large Fibonacci number. In particular, we show that all trees with n edges and Fibonacci number > 2n−1 + 5 have diameter ≤ 4 and determine the order of these trees with respect to their Fibonacci numbers. Furthermore, it is shown that the average Fibonacci number of a star-like ...
متن کاملNotes on Fibonacci Partitions
Abstract. Let f1 = 1, f2 = 2, f3 = 3, f4 = 5, . . . be the sequence of Fibonacci numbers. It is well known that for any natural n there is a unique expression n = fi1 + fi2 + · · · + fiq , such that ia+1 − ia > 2 for a = 1, 2, . . . , q− 1 (Zeckendorf Theorem). By means of it we find an explicit formula for the quantity Fh(n) of partitions of n with h summands, all parts of them are the pairwis...
متن کاملCompositions, Partitions, and Fibonacci Numbers
A bijective proof is given for the following theorem: the number of compositions of n into odd parts equals the number of compositions of n + 1 into parts greater than one. Some commentary about the history of partitions and compositions is provided.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: TEMA - Tendências em Matemática Aplicada e Computacional
سال: 2006
ISSN: 2179-8451,1677-1966
DOI: 10.5540/tema.2006.07.01.0119