Convex $(0,1)$-Matrices and Their Epitopes

TL;DR

This paper studies convex (0,1)-matrices with consecutive ones in rows and columns, extending the concept of ranked essential sets to these matrices and showing their uniqueness within certain classes.

Contribution

It extends the notion of ranked essential sets to convex matrices and proves their uniqueness in classifying matrices with fixed row and column sums.

Findings

Ranked essential sets uniquely determine convex matrices in the class.

The paper characterizes convex matrices with given row and column sums.

Results contribute to discrete tomography and matrix classification.

Abstract

We investigate $(0,1)$-matrices that are {\em convex}, which means that the ones are consecutive in every row and column. These matrices occur in discrete tomography. The notion of ranked essential sets, known for permutation matrices, is extended to convex sets. We show a number of results for the class $\mc{C}(R,S)$ of convex matrices with given row and column sum vectors $R$ and $S$. Also, it is shown that the ranked essential set uniquely determines a matrix in $\mc{C}(R,S)$.