科研之友
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摘要
Daniel A. Marcus claimed in a "Note added in proof" to his 1984 paper on positively k-spanning vector configurations that some minimal positively k-spanning vector configurations in m-dimensional space have more than 2km elements, but the example he found (for k = 2 and m = 12) seems to be lost.
We produce such an example by applying Gale duality, a linear algebra technique developed by Micha Perles in the sixties, to a result on illuminated polytopes by Peter Mani from 1974. Our example has exactly the parameters claimed by Marcus.
Conversely, we show how results on positively k-spanning vector configurations, again via Gale duality, can be used to solve a problem by Mani on nonsimplicial illuminated polytopes.
- 出版日期2011-7
