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The solution to a matroid problem of Knuth

✍ Scribed by Robert E. Bixby


Publisher
Elsevier Science
Year
1978
Tongue
English
Weight
167 KB
Volume
21
Category
Article
ISSN
0012-365X

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✦ Synopsis


In thig ncrte we answer a question posed by Knuth in his recent paper "Random matroids".

E"rtrutb des&.xs in [2] an algorithm which, subject to certain arbitrary choices, is ~&D&C of constructing any matroid. In effect, this algorithm shows how to ob~ai$d '"erectians? (as defined by Crapo [l]) of a given matroid. This has also -been &lane by Roberts [3], althoqgh Knuth's work shows that the procedure in can be @mpMied.

Her&e will be interested only in a derivative of Knuth's algorithm, namely the s~-@td "free completion (erection) of a clutter". In [2j it is asked, roughly speaking, whether or not this "free completion" can be used to generate nonmat-


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