König's theorem and bimatroids
type: Item
instance of: scholarly article
title: König's theorem and bimatroids
zbMATH Open document ID: 0816.05021
DOI: 10.1016/0024-3795(94)90410-3
published in: Linear Algebra and its Applications
publication date: 1995-07-13T00:00:00Z
review text: The author generalizes various extensions of König's theorem, to mixed matrices by Murota, and a determinantal version due to \textit{D. J. Hartfiel} and \textit{R. Loewy} [Linear Multilinear Algebra 16, 155-166 (1964; Zbl 0551.15002)]. A minimax theorem is proven for the rank function of a bimatroid (or linking system).
reviewed by: András Recski
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 15B36
zbMATH DE Number: 720483
zbMATH Keywords: König's theorem
zbMATH Keywords: minimax theorem
zbMATH Keywords: rank function
zbMATH Keywords: bimatroid
author: R. B. Bapat
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)90410-3
OpenAlex ID: W2039352784
cites work: Combinatorial matrix theory
cites work: Systems of distinct representatives and linear algebra
cites work: Q3831127
cites work: A determinantal version of the frobenius-könig theorem
cites work: Bimatroids and invariants
cites work: Q3880849
cites work: Permanents
cites work: Transversal theory. An account of some aspects of combinatorial mathematics
cites work: Systems analysis by graphs and matroids. Structural solvability and controllability
cites work: Principal structure of layered mixed matrices
cites work: On the Smith Normal Form of Structured Polynomial Matrices
cites work: Q4281309
cites work: Matroid theory and its applications in electric network theory and in statics
cites work: Q4166767
cites work: Matroids and linking systems
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description: scientific article; zbMATH DE number 720483