Kevin G. Hare

activity

20102026

collaborators

5 papers

math.NT2026

Non-Expansive Matrix Based number Systems

Adam Blažek, Kevin G. Hare, Edita Pelantová

An integer $d$ -dimensional vector is usually represented by $d$ strings, which express the value of each component separately. This article is devoted to number systems that allow…

math.NT2026

Parry order of Parry numbers

Kevin G Hare, Hachem Hichri

We introduce the \emph{Parry order} $Ord_{P} (β)$ , defined as the largest integer $n$ for which $β^{n}$ is a Parry number. This leads to a natural partition of the set of Perro…

math.NT2025

Greedy Beta-expansions for families of Salem numbers

Kevin G. Hare, Liam Orovec

We give criteria for finding the greedy $β$ -expansion for $1$ for families of Salem numbers that approach a given Pisot number. We show that these expansions are related to the gre…

math.DS2024

Totally real algebraic numbers in generalized Mandelbrot set

Kevin G. Hare, Chatchai Noytaptim

In this article, we study some potential theoretical and topological aspects of the generalized Mandelbrot set introduced by Baker and DeMarco. For $α$ real, we study the set of al…

math.NT2010

The sum of digits of $n$ and $n^{2}$

K. G. Hare, S. Laishram, T. Stoll

Let $s_{q} (n)$ denote the sum of the digits in the $q$ -ary expansion of an integer $n$ . In 2005, Melfi examined the structure of $n$ such that $s_{2} (n) = s_{2} (n^{2})$ . We extend this stu…

Non-Expansive Matrix Based number Systems

Parry order of Parry numbers

Greedy Beta-expansions for families of Salem numbers

Totally real algebraic numbers in generalized Mandelbrot set

The sum of digits of n and n2

The sum of digits of $n$ and $n^{2}$