Kevin G. Hare

activity

20102023

most citedGrowth degree classification for finitely generated semigroups of integer matrices

4 citations · 8 across the 9 of their papers we have counts for

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Showing 2014Show all

3 papers · 1 filter

math.NT2014★ 4 cited

Growth degree classification for finitely generated semigroups of integer matrices

Jason P. Bell, Michael Coons, Kevin G. Hare

Let $A$ be a finite set of $d \times d$ matrices with integer entries and let $m_{n} (A)$ be the maximum norm of a product of $n$ elements of $A$ . In this…

math.NT2014★ 1 cited

The minimal growth of a $k$ -regular sequence

Jason P. Bell, Michael Coons, Kevin G. Hare

We determine a lower gap property for the growth of an unbounded $\mathbb{Z}$-valued $k$-regular sequence. In particular, if $f:\mathbb{N}\to\mathbb{Z}$ is an unbounded $k$…

math.NT2014★ 2 cited

There are no two non-real conjugates of a Pisot number with the same imaginary part

Artūras Dubickas, Kevin G. Hare, Jonas Jankauskas

We show that the number $α = (1 + 3 + 25) /2$ with minimal polynomial $x^{4} - 2 x^{3} + x - 1$ is the only Pisot number whose four distinct conjugates $α_{1}, α_{2}, α_{3}, α_{4}$ satisfy the ad…

Growth degree classification for finitely generated semigroups of integer matrices

The minimal growth of a k-regular sequence

There are no two non-real conjugates of a Pisot number with the same imaginary part

The minimal growth of a $k$ -regular sequence