Polygons as Sections of Higher-Dimensional Polytopes
نویسندگان
چکیده
We show that every heptagon is a section of a 3-polytope with 6 vertices. This implies that every n-gon with n > 7 can be obtained as a section of a (2 + ⌊ n 7 ⌋ )dimensional polytope with at most ⌈ 6n 7 ⌉ vertices; and provides a geometric proof of the fact that every nonnegative n ×m matrix of rank 3 has nonnegative rank not larger than ⌈ 6min(n,m) 7 ⌉ . This result has been independently proved, algebraically, by Shitov (J. Combin. Theory Ser. A 122, 2014).
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عنوان ژورنال:
- Electr. J. Comb.
دوره 22 شماره
صفحات -
تاریخ انتشار 2015