Kevin G. Hare

activity

20102026

collaborators

Showing math.NTShow all

4 papers · 1 filter

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.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

The sum of digits of n and n2

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