Maximal minors and their leading terms
type: Item
instance of: scholarly article
title: Maximal minors and their leading terms
zbMATH Open document ID: 0776.13009
author: Bernd Sturmfels
author: Andrei Zelevinsky
published in: Advances in Mathematics
publication date: 1993-06-29T00:00:00Z
review text: The authors study the Newton polyhedra of the polynomial given by the product of all maximal minors of a \(m \times n\) matrix of indeterminates \(X=(x_{ij})\). It is a polytope in \(\mathbb{R}^{mn}\). The description of this polytope is well known in the following cases: If \(m=n\) it is the Birkhoff polytope of doubly stochastic \(n \times n\) matrices. -- If \(m=2\) it is the convex hull in \(\mathbb{R}^{2n}\) of all \(n!\) matrices obtained from \(\begin{pmatrix} n-1 & n-2 & \ldots & 1 & 0 \\ 0& 1 & \ldots & n-2 & n-1 \end{pmatrix}\) by permuting columns. The description of this polytope is really difficult and interesting. The authors give some motivations and applications.
Mathematics Subject Classification ID: 13C40
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 14M25
Mathematics Subject Classification ID: 14M12
Mathematics Subject Classification ID: 14N10
zbMATH DE Number: 221239
zbMATH Keywords: maximal minors of matrix of indeterminates
zbMATH Keywords: Newton polyhedra
reviewed by: Marcel Morales
MaRDI profile type: Publication
full work available at URL: aima.1993.1013
OpenAlex ID: W1990398263
Wikidata QID: Q121745518
DOI: 10.1006/AIMA.1993.1013
description: scientific article; zbMATH DE number 221239