Author

István Tomon

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Preprint Sep 2026

Tight bounds for positive discrepancy via eigenvalues

Given an $n\times n$ symmetric matrix $M$ with largest eigenvalue $\lambda_1\geq 0$, it is easy to show that the solution of the optimisation problem $\max_{v\in [-1,1]^n}v^TMv$ is at most $\lambda_1 n$. We prove the following converse: if every $n'\times n'$ principal submatrix of $M$ has maximal eigenvalue at least $...

Oliver Janzer, István Tomon, Fredy Yip · 0 citations

Preprint Aug 2026

Discrepancy of geometric incidences

We study the combinatorial (red-blue) discrepancy of finite point sets with respect to hyperplanes and, more generally, bounded-complexity affine algebraic sets. We prove that every $n$-point set in a real Euclidean space admits a red-blue coloring for which every affine algebraic set of dimension at most $D$ and degre...

A. Adıbelli, István Tomon · 1 citation