Takashi Hirotsu

collaborators

6 papers

math.CO2026

Relative Ehrhart theory I: relative Ehrhart eventual polynomials

Takashi Hirotsu

Classical Ehrhart theory measures the discrete capacity of a convex rational (or integral) polytope $P$ by counting the number of lattice points in the $t$ -th dilate $tP$ of $P$ . I…

math.CO2026

Several properties of summatory Ehrhart polynomials and series of convex lattice polytopes

Takashi Hirotsu

In this article, for a convex lattice polytope, we further investigate the summatory function of its Ehrhart polynomial, which is called the summatory Ehrhart polynomial, and intro…

math.CO2026

Horizontal miniatures and normal-sized miniatures of convex lattice polytopes

Takashi Hirotsu

Let $n,$ $d,$ and $r$ be integers such that $0 \leq r \leq d \leq n,$ and let $P \subset R^{n}$ be a $d$ -dimensional convex lattice polytope. In this article, we prove that t…

math.NT2026

Algebraic Characterizations of Angle Multisections over Rings

Takashi Hirotsu

Let $n,$ $m \geq 2$ be integers, and let $R$ be a subring of $R$ with field of fractions $F .$ In this article, we generalize the rational angle bisection problem previously…

math.NT2025

Rational Angle Bisection Problem in Higher Dimensional Spaces and Incenters of Simplices over Fields

Takashi Hirotsu

In this article, we generalize the following problem, which is called the rational angle bisection problem, to the $n$ -dimensional space $k^{n}$ over a subfield $k$ of $R$ : i…

math.CO2025

Average-sized miniatures and normal-sized miniatures of lattice polytopes

Takashi Hirotsu

Let $d \geq 0$ be an integer and let $P \subset R^{d}$ be a $d$ -dimensional lattice polytope. We call a polytope $M \subset R^{d}$ such that $M \subset P$ and $M \sim P…