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ℓ-matrices and a characterization of binary matroids

✍ Scribed by Robert E. Bixby

Publisher: Elsevier Science
Year: 1974
Tongue: English
Weight: 566 KB
Volume: 8
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(74)90060-0

No coin nor oath required. For personal study only.

✦ Synopsis

1+ Introductim

2. &tnatrsids

An Z-nt~rfpis is 8 @-I matrix having thk. I+ 7 .Fyaty tha? some permuta-tion of its distinct ~ofutnns is the matrix J: I,* fair some intttgcr r 2 '1. JP is the r * r matrix of all 1's and lr is thbz F X r identity. Given an [-maitrix with r rows. the follc:wing propertie!; arts immediate from the definition: t'vt'v ic.stt:mn cont3ins exactly ant 0, every ruw contains at iejst one 0. ifr = 3, then the symmetric' differenoc of ;tny two rows is the third; and ifr > 3. then the symrnetrk difference of no two rows contains another row.

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