Koki Furukawa

activity

20242026

collaborators

4 papers

math.CO2026

A note on distinct volume subsets problem

Koki Furukawa

For $2 \leq a \leq d + 1$ , what is the largest integer $H_{a, d} (n)$ such that every set of $n$ points in $R^{d}$ with no $a$ points on a common $(a - 2)$ -flat contains a subset…

math.CO2026

Simplex volumes in hyperplane arrangements

Koki Furukawa

We study the dual variants of the ErdÅs's distinct distances and unit distance problems. Instead of considering distances determined by points, we consider simplex volumes determi…

math.CO2025

Big convex polytopes or rich hyperplanes

Koki Furukawa

For natural numbers $n$ and $l > d \geq 2$ , let $E S_{d} (l, n)$ be the minimum $N$ such that any set of at least $N$ points in $R^{d}$ contains either $l$ points contained in a…

math.CO2024

Happy Ending or Many Concurrent Lines

Koki Furukawa

For each $n \geq 2$ , $l \geq 3$ , let $E S_{L} (l, n)$ be the minimum $N$ such that every family of $N$ -lines in the plane contains either $l$ concurrent lines or $n$ lines in convex…