A Generalization of Zeckendorf's Theorem Via Circumscribed m-gons

Description
Zeckendorf’s theorem states that every positive integer can be uniquely decom- posed as a sum of nonconsecutive Fibonacci numbers, where the Fibonacci numbers satisfy F1 = 1, F2 = 2, and Fn = Fn−1+Fn−2 for n ≥ 3. The distribution of the number of summands in such a decomposition converges to a Gaussian, the gaps between summands converge to geometric decay, and the distribution of the longest gap is similar to that of the longest run of heads in a biased coin; these results also hold more generally, though for technical reasons previous work is needed to assume the coefficients in the recurrence relation are nonnegative and the first term is positive.

In collections

File details
ID Label Size Mimetype Created
OBJ MC314_022_FourakisEva_GeneralizationZeckendorfsTheoremmgons.pdf 681.65 KiB application/pdf 2020-05-27
TN TN 3.57 KiB image/jpeg 2020-05-27