Journal of Integer Sequences, Vol. 19 (2016), Article 16.4.5

Additive Functions on the Greedy and Lazy Fibonacci Expansions

Kalyan Chakraborty
Harish-Chandra Research Institute
Chhatnag Road, Jhunsi
Allahabad, UP 211019

Imre Kátai and Bui Minh Phong
Computer Algebra Department
Eötvös Loránd University
Pázmány Péter Sétány I/C
1117 Budapest


We find all complex-valued functions that are additive with respect to both the greedy and the lazy Fibonacci expansions. We take it a little further by considering the subsets of these functions that are also multiplicative. In the final section we extend these ideas to Tribonacci expansions.

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Received July 7 2015; revised versions received October 18 2015; October 29 2015; December 7 2015; April 18 2016; April 24 2016. Published in Journal of Integer Sequences, May 9 2016.

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