Geodesic
Additive functions on the greedy and lazy Fibonacci expansions
Journal of integer sequences, Tome 19 (2016) no. 4
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.
Classification : 11A25, 11A67
Keywords: Fibonacci sequence, tribonacci sequence, greedy expansion, lazy expansion 
@article{JIS_2016__19_4_a0,
     author = {Chakraborty,  Kalyan and K\'atai,  Imre and Phong,  Bui Minh},
     title = {Additive functions on the greedy and lazy {Fibonacci} expansions},
     journal = {Journal of integer sequences},
     year = {2016},
     volume = {19},
     number = {4},
     zbl = {1415.11011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_4_a0/}
}
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Chakraborty,  Kalyan; Kátai,  Imre; Phong,  Bui Minh. Additive functions on the greedy and lazy Fibonacci expansions. Journal of integer sequences, Tome 19 (2016) no. 4. http://geodesic.mathdoc.fr/item/JIS_2016__19_4_a0/