: The La Roche Site . J. J. Hoffman. ; Bighorn Canyon Archeology . Wilfred M. Husted.

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On a Conjecture of a . J . Hoffman

The following question was recently raised by A. J. Hoffman [2]: "If P is a d-polytope, i>0 an integer and &,••*, C* closed convex sets in P, such that every /-flat that meets P meets Uf=i d; do there exist polytopes Di, • • • , Dk, with DiQd for all 1 ̂ i^k, such that if a ¿-flat meets P, it meets Uf_x 7>,?" The purpose of this note is to give a counterexample to this conjecture, with d = 3, t ...

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On a Conjecture of A. J. Hoffman. Ii

It is proved that certain incidence relations of hyperplanes and closed convex sets in a rf-polytope can be preserved while replacing these sets by suitable polytopal subsets. The purpose of this paper is to prove Theorem 1. IfP is a d-polytope in Ed and Cx, * • •, Cj are closed convex subsets of P, such that every hyperplane that meets P meets (J¿=i Q> tnen there exist poly topes Dx, • • ■ , D...

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ژورنال

عنوان ژورنال: American Anthropologist

سال: 1970

ISSN: 0002-7294,1548-1433

DOI: 10.1525/aa.1970.72.3.02a00720