Properties of the multiway discrepancy

TL;DR

This paper investigates the properties of multiway discrepancy in nonnegative matrices, proving its continuity and exploring its behavior in special cases, while conjecturing about its monotonicity with respect to k.

Contribution

It introduces new theoretical insights into multiway discrepancy, including continuity proofs and conjectures on monotonicity, expanding understanding of matrix and graph properties.

Findings

Proved the continuity of multiway discrepancy.

Analyzed multiway discrepancy in special matrices and graphs.

Conjectured that k-way discrepancy is monotonic in k.

Abstract

Some properties of the multiway discrepanc of rectangular matrices of nonnegative entries are discussed. We are able to prove the continuity of this discrepancy, as well as some statements about the multiway discrepancy of some special matrices and graphs. We also conjecture that the k-way discrepancy is monotonic in k.