H. Alpert (2009):
Differences of multiple Fibonacci numbers.
INTEGERS 9,
doi:10.1515/INTEG.2009.061.
Paper #A57.
J. Berstel (2001):
An exercise on Fibonacci representations.
RAIRO Inform. Théor. App. 35,
pp. 491–498,
doi:10.1051/ita:2001127.
J. L. Brown, Jr. (1965):
A new characterization of the Fibonacci numbers.
Fibonacci Quart. 3(1),
pp. 1–8.
J. L. Brown, Jr. (1969):
Unique representation of integers as sums of distinct Lucas numbers.
Fibonacci Quart. 7,
pp. 243–252.
V. Bruyère, G. Hansel, C. Michaux & R. Villemaire (1994):
Logic and p-recognizable sets of integers.
Bull. Belgian Math. Soc. 1,
pp. 191–238,
doi:10.36045/bbms/1103408547.
Corrigendum,ıt Bull. Belg. Math. Soc. 1 (1994), p. 577.
J. R. Büchi (1960):
Weak second-order arithmetic and finite automata.
Zeitschrift für mathematische Logik und Grundlagen der Mathematik 6,
pp. 66–92,
doi:10.1002/malq.19600060105.
Reprinted in S. Mac Lane and D. Siefkes, eds.,ıt The Collected Works of J. Richard Büchi, Springer-Verlag, 1990, pp. 398–424.
M. W. Bunder (1992):
Zeckendorf representations using negative Fibonacci numbers.
Fibonacci Quart. 30,
pp. 111–115.
L. Carlitz, R. Scoville & V.E. Hoggatt, Jr. (1972):
Fibonacci representations of higher order.
Fibonacci Quart. 10,
pp. 43–69, 94.
P. Hajnal (2023):
A short note on numeration systems with negative digits allowed.
Bull. Inst. Combin. Appl. 97,
pp. 54–66.
J. E. Hopcroft & J. D. Ullman (1979):
Introduction to Automata Theory, Languages, and Computation.
Addison-Wesley.
A. F. Horadam (1993):
Zeckendorf representations of positive and negative integers by Pell numbers.
In: G. E. Bergum, A. N. Philippou & A. F. Horadam: Applications of Fibonacci Numbers 5.
Kluwer,
pp. 305–316,
doi:10.1007/978-94-011-2058-6_29.
C. G. Lekkerkerker (1952):
Voorstelling van natuurlijke getallen door een som van getallen van Fibonacci.
Simon Stevin 29,
pp. 190–195.
H. Mousavi (2016):
Automatic theorem proving in Walnut.
Arxiv preprint arXiv:1603.06017 [cs.FL], available at http://arxiv.org/abs/1603.06017.
H. Mousavi, L. Schaeffer & J. Shallit (2016):
Decision Algorithms for Fibonacci-Automatic Words, I: Basic Results.
RAIRO Inform. Théor. App. 50,
pp. 39–66,
doi:10.1051/ita/2016010.
A. Ostrowski (1922):
Bemerkungen zur Theorie der Diophantischen Approximationen.
Abh. Math. Sem. Hamburg 1,
pp. 77–98,250–251,
doi:10.1007/BF02940595.
Reprinted inıt Collected Mathematical Papers, Vol. 3, pp. 57–80.
H. Park, B. Cho, D. Cho, Y. D. Cho & J. Park (2020):
Representations of integers as sums of Fibonacci numbers.
Symmetry 12(10),
doi:10.3390/sym12101625.
Paper 1625.
N. Robbins (1996):
Fibonacci partitions.
Fibonacci Quart. 34,
pp. 306–313.
J. Shallit (2021):
Robbins and Ardila meet Berstel.
Inform. Process. Lett. 167,
doi:10.1016/j.ipl.2020.106081.
Paper 106081.
J. Shallit (2022):
The Logical Approach to Automatic Sequences: Exploring Combinatorics on Words with Walnut.
London Math. Soc. Lecture Notes Series 482.
Cambridge University Press,
doi:10.1017/9781108775267.
E. Zeckendorf (1972):
Représentation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas.
Bull. Soc. Roy. Liège 41,
pp. 179–182.
eptcs@eptcs.org