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

Access to Document

10.1090/S0002-9939-1971-0275282-1

Cite this

@article{7d98aaf90be94cc389c4fe5a660072e4,

title = "On a conjecture of a.J.Hoffman",

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 {\textquoteleft} 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{\textquoteleft} s. This is a counterexample to a conjecture of A. J. Hoffman.",

keywords = "Affine t-flat, Closed convex set, Convex d-polytype, Convex planar curve",

author = "Joseph Zaks",

year = "1971",

month = jan,

doi = "10.1090/S0002-9939-1971-0275282-1",

language = "English",

volume = "27",

pages = "122--125",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "1",

}

TY - JOUR

T1 - On a conjecture of a.J.Hoffman

AU - Zaks, Joseph

PY - 1971/1

Y1 - 1971/1

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=84968521941&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1971-0275282-1

DO - 10.1090/S0002-9939-1971-0275282-1

M3 - Article

AN - SCOPUS:84968521941

SN - 0002-9939

VL - 27

SP - 122

EP - 125

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 1

ER -

On a conjecture of a.J.Hoffman

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this