A note on the discrepancy of matrices with bounded row and column sums

TL;DR

This paper extends a known discrepancy result for hypergraphs to real matrices with bounded row and column sums, using probabilistic methods.

Contribution

It generalizes the folklore discrepancy result from hypergraphs to matrices with bounded sums, broadening the scope of the original theorem.

Findings

Generalization of discrepancy bounds to matrices

Application of Lovasz local lemma in matrix context

Potential implications for combinatorial matrix analysis

Abstract

A folklore result uses the Lovasz local lemma to analyze the discrepancy of hypergraphs with bounded degree and edge size. We generalize this result to the context of real matrices with bounded row and column sums.