科研之友
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摘要
The colourful simplicial depth problem in dimension d is to find a configuration of (d+1) sets of (d+1) points such that the origin is contained in the convex hull of each set, or colour, but contained in a minimal number of colourful simplices generated by taking one point from each set. A construction attaining d(2) + 1 simplices is known, and is conjectured to be minimal. This has been confirmed up to d = 3, however the best known lower bound for d %26gt;= 4 is left perpendicular(d+1)(2)/2right perpendicular. In this note, we use a branching strategy to improve the lower bound in dimension 4 from 13 to 14.
- 出版日期2013-3
