Upper Bounds for Digitwise Generating Functions of Powers of Two: A Problem and a Matrix Representation
Combinatorics
2025-10-22 v1 Number Theory
Probability
Abstract
This short note studies the asymptotic behavior of a generating function associated with the decimal expansion of . Our aims are twofold: (i) to present a problem on the best possible upper bound for this behavior, and (ii) to introduce a matrix representation that is useful for its analysis. The representation corresponds to a finite-state transfer operator; analytic and dynamical aspects are not pursued here.
Cite
@article{arxiv.2510.18414,
title = {Upper Bounds for Digitwise Generating Functions of Powers of Two: A Problem and a Matrix Representation},
author = {Hideaki Noda},
journal= {arXiv preprint arXiv:2510.18414},
year = {2025}
}