Revisiting the spreading and covering numbers

Details Revisiting the spreading and covering numbers Revisiting the spreading and covering numbers

2011-09-27

arxiv.org/abs/1109.5847v1

Mathematics

Commutative Algebra

16 pages; needs the package tkz-graph.sty

Scientific paper

We revisit the problem of computing the spreading and covering numbers. These numbers were first introduced by Geramita, Gregory, and Roberts to study the Ideal Generation Conjecture, a conjecture concerning sets of points in a projective space. Both the spreading number and covering number can be reformulated as a graph theory question. We describe some new approaches to computing or bounding these numbers. In addition, we show a surprising connection to some of the spreading numbers to the sequence A053307 in the On-Line Encyclopedia of Integer Sequences.

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