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On Supmodular Matrices

Shmuel Onn

Abstract

We consider the problem of determining which matrices are permutable to be supmodular. We show that for small dimensions any matrix is permutable by a universal permutation or by a pair of permutations, while for higher dimensions no universal permutation exists. We raise several questions including to determine the dimensions in which every matrix is permutable.

On Supmodular Matrices

Abstract

We consider the problem of determining which matrices are permutable to be supmodular. We show that for small dimensions any matrix is permutable by a universal permutation or by a pair of permutations, while for higher dimensions no universal permutation exists. We raise several questions including to determine the dimensions in which every matrix is permutable.
Paper Structure (2 sections, 4 theorems, 14 equations)

This paper contains 2 sections, 4 theorems, 14 equations.

Table of Contents

  1. Introduction
  2. Proofs

Key Result

Theorem 1.2

Let $A$ be any $m\times n$ real matrix with $m\leq n$. Then we have:

Theorems & Definitions (5)

  • Definition 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Lemma 2.1
  • Lemma 2.2