Skand Parvatikar

collaborators

3 papers

math.MG2026

Unbalancing unit vectors

Zilin Jiang, Jeck Lim, Skand Parvatikar

We show that for every $n$ unit vectors $v_{1}, \dots, v_{n}$ in the $d$ -dimensional Euclidean space, there exist signs $ε_{1}, \dots, ε_{n} \in {\pm 1}$ such that $\…

math.CO2026

On colorful Helly numbers and the growth of Tverberg numbers

Chaya Keller, Skand Parvatikar, Tuan Tran

In this paper, we obtain new upper and lower bounds on the colorful Helly number and the Tverberg number in an abstract convexity space with Radon number $r$ . We prove an upper bou…

math.CO2026

Rainbow cycles in triangle-free graphs

Andrzej Czygrinow, Skand Parvatikar

Let $G = (V, E)$ be an edge-colored graph, and let $δ^{c} (G) = min_{v \in V} {d^{c} (v)}$ where $d^{c} (v)$ is the number of colors on edges incident to a vertex $v$ . We show that fo…