Unique representability and matroid reconstruction
type: Item
instance of: scholarly article
title: Unique representability and matroid reconstruction
zbMATH Open document ID: 1031.05033
DOI: 10.1016/S0196-8858(02)00500-6
author: William P. Miller
published in: Advances in Applied Mathematics
publication date: 2003-09-15T00:00:00Z
review text: A matroid is deletion reconstructible (resp. \(k\)-reconstructible) if it is determined by its set of deletions (resp. \(k\)-element deletions). This article gives two methods for showing deletion reconstructibility of matroids that are uniquely GF\((q)\)-representable. The first one uses inclusion-exclusion and extends techniques in graph edge-reconstruction of Lovász. The second one extends techniques of Nash-Williams and is based on counting automorphisms. Bounds that are exponential in terms of rank are given for the number of points needed to ensure that a representable matroid is reconstructible, and quadratic bounds are given for binary and ternary matroids.
reviewed by: David Forge
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 05C60
zbMATH DE Number: 1981411
zbMATH Keywords: matroid
zbMATH Keywords: reconstruction
zbMATH Keywords: unique representability
zbMATH Keywords: affine geometry
zbMATH Keywords: projective geometry
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1981411