Noah Kravitz

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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.CO2024

Bender--Knuth Billiards in Coxeter Groups

Grant Barkley, Colin Defant, Eliot Hodges +2

Let $(W, S)$ be a Coxeter system, and write $S = {s_{i} : i \in I}$ , where $I$ is a finite index set. Fix a nonempty convex subset $L$ of $W$ . If $W$ is of type $A$ , then $\mat…

math.CO2024

Foot-Sorting for Socks

Colin Defant, Noah Kravitz

If your socks come out of the laundry all mixed up, how should you sort them? We introduce and study a novel foot-sorting algorithm that uses feet to attempt to sort a sock orderin…

math.CO2024

Rainbow Stackings of Random Edge-Colorings

Noga Alon, Colin Defant, Noah Kravitz

A rainbow stacking of $r$ -edge-colorings $I ¨ _{1}, \dots, I ¨ _{m}$ of the complete graph on $n$ vertices is a way of superimposing $I ¨ _{1}, \dots, I ¨ _{m}$ so that no edges of the same colo…