Ruben Carpenter

collaborators

3 papers

math.CO2026

Sets with Few Subset Sums

Ruben Carpenter, Colin Defant, Noah Kravitz

It is a classical fact that every $n$ -element set of positive reals has at least $(2 n + 1) + 1$ distinct subset sums, with equality exactly for homogeneous arithmetic progressi…

math.CO2026

On the number of permutation-twisted dot products

Ruben Carpenter, Colin Defant, Noah Kravitz

Let $K$ be a field of characteristic $0$ . For each choice of distinct $a_{1}, \dots, a_{n} \in K$ and distinct $b_{1}, \dots, b_{n} \in K$ , consider the sum $S=\…

math.PR2025

Taming Irrationality: An Invariance Principle for the Random Billiard Walk

Ruben Carpenter

The random billiard walk is a stochastic process $(L_{t})_{t \geq 0}$ in which a laser moves through the Coxeter arrangement of an affine Weyl group in $R^{d}$ , reflecting at e…