Browsing University of Waterloo by Subject "numeration systems"
Now showing items 1-3 of 3
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The number of valid factorizations of Fibonacci prefixes
(Elsevier, 2019-07-05)We establish several recurrence relations and an explicit formula for V(n), the number of factorizations of the length-n prefix of the Fibonacci word into a (not necessarily strictly) decreasing sequence of standard Fibonacci ... -
The number of valid factorizations of Fibonacci prefixes
(Elsevier, 2019-07-05)We establish several recurrence relations and an explicit formula for , the number of factorizations of the length-n prefix of the Fibonacci word into a (not necessarily strictly) decreasing sequence of standard Fibonacci ... -
Proving Properties of Fibonacci Representations via Automata Theory
(University of Waterloo, 2024-01-22)In this work, we introduce a novel framework for mechanically testing the completeness and unambiguity of Fibonacci-based representations via automata theory. We call a representation (or a number system) complete and ...