Optimal expansions of Kakeya sequences
Anna Chiara Lai, Paola Loreti
TL;DR
This paper studies the best possible ways to represent real numbers using Kakeya sequences, generalizing non-integer base expansions and exploring their uniqueness and optimality conditions.
Contribution
It characterizes optimal expansions of Kakeya sequences and establishes conditions for the uniqueness of such expansions.
Findings
Characterization of optimal Kakeya sequence expansions
Conditions for unique expansions in Kakeya sequences
Analysis of redundancy phenomena in these expansions
Abstract
We investigate optimal expansions of Kakeya sequences for the representation of real numbers. Expansions of Kakeya sequences generalize the expansions in non-integer bases and they display analogous redundancy phenomena. In this paper, we characterize optimal expansions of Kakeya sequences, and we provide conditions for the existence of unique expansions with respect to Kakeya sequences.
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Taxonomy
TopicsBenford’s Law and Fraud Detection · Computability, Logic, AI Algorithms · Financial Risk and Volatility Modeling