On a conjecture of a.J.Hoffman

Joseph Zaks

doi:10.1090/S0002-9939-1971-0275282-1

On a conjecture of a.J.Hoffman

Research output: Contribution to journal › Article › peer-review

Abstract

A 3-polytope P and four closed convex sets C1,;…, C4 in P are described, having the following property: every line which meets P meets at least one of the Ci ‘ s, and for every collection of polytopes D1, …, D4, with Di⊆ Ci for all 1≦ i≦ 4, there exists a line which meets P and misses all of the Di‘ s. This is a counterexample to a conjecture of A. J. Hoffman.

Original language	English
Pages (from-to)	122-125
Number of pages	4
Journal	Proceedings of the American Mathematical Society
Volume	27
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1971-0275282-1
State	Published - Jan 1971
Externally published	Yes

Keywords

Affine t-flat
Closed convex set
Convex d-polytype
Convex planar curve

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-1971-0275282-1

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AB - A 3-polytope P and four closed convex sets C1,;…, C4 in P are described, having the following property: every line which meets P meets at least one of the Ci ‘ s, and for every collection of polytopes D1, …, D4, with Di⊆ Ci for all 1≦ i≦ 4, there exists a line which meets P and misses all of the Di‘ s. This is a counterexample to a conjecture of A. J. Hoffman.

KW - Affine t-flat

KW - Closed convex set

KW - Convex d-polytype

KW - Convex planar curve

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On a conjecture of a.J.Hoffman

Abstract

Keywords

ASJC Scopus subject areas

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