The solution to a matroid problem of Knuth
β Scribed by Robert E. Bixby
- Publisher
- Elsevier Science
- Year
- 1978
- Tongue
- English
- Weight
- 167 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ 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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